Mathematics of Computation This journal publishes research articles in computational mathematics. Areas covered include numerical analysis, with emphasis on the mathematical analysis and development of methods, computational number theory and algebra, and related fields. Table errata and reviews of books in areas related to computational mathematics are also included. Submission information. See Information for Authors at the end of this issue. Subscription information. Mathematics of Computation is published quarterly. Be- ginning in January 1996 Mathematics of Computation is accessible from e-MATH via the World Wide Web at the URL http : //www.ams.org/publications/. Subscription prices for Volume 65 (1996) are as follows: for paper delivery, $290 list, $232 institutional mem- ber, $261 corporate member, $189 MAA & SIAM members; $174 individual member; for electronic delivery, $261 list, $209 institutional member, $235 corporate member, $170 MAA & SIAM members, $157 individual member; for combination paper and electronic delivery, $334 list, $267 insititutional member, $301 corporate member, $217 MAA & SIAM members, $200 individual member. If ordering the paper version, add $9 for sur- face delivery outside the United States and India; $18 to India. Expedited delivery to destinations in North America is $13; elsewhere $40. Back number information. For back issues see the AMS Catalog of Publications. Subscriptions and orders should be addressed to the American Mathematical Society, P.O. Box 5904, Boston, MA 02206-5904. All orders must be accompanied by payment. Other correspondence should be addressed to P.O. Box 6248, Providence, RI 02940-6248. Unpublished Mathematical Tables. The editorial office of the journal maintains a repository of Unpublished Mathematical Tables (UMT). When a table is deposited in the UMT repository a brief summary of its contents is published in the section Reviews and Descriptions of Tables and Books. Upon request, the chairman of the editorial committee will supply copies of any table for a nominal cost per page. All tables and correspondence concerning the UMT should be sent to Lars B. Wahlbin, Chairman, Editorial Committee, Mathematics of Computation, Center for Applied Mathematics, 657 Frank H. T. Rhodes Hall, Cornell University, Ithaca, NY 14853. Copying and reprinting. Material in this journal may be reproduced by any means for educational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents and provided that the customary acknowledgment of the source is given. This consent does not extend to other kinds of copying for general distribution, for advertising or promotional purposes, or for resale. Requests for permission for commercial use of material should be addressed to the Assistant to the Publisher, American Mathematical Society, P.O. Box 6248, Providence, RI 02940-6248. Requests can also be made by e-mail to [email protected]. Excluded from these provisions is material in articles for which the author holds copy- right. In such cases, requests for permission to use or reprint should be addressed directly to the author(s). (Copyright ownership is indicated in the notice in the lower right-hand corner of the first page of each article.)

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c 1996 by the American Mathematical Society. All rights reserved. This journal is indexed in Science Citation Index r, SciSearchr, Research Alert r, CompuMath Citation Index r, and Current Contentsr/Physical, Chemical & Earth Sciences. ∞ The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. 10987654321 010099989796 INDEX TO VOLUME 65 (1996)

Acciaro, Vincenzo. Solvability of norm equations over cyclic number fields of prime degree, 1663 Anglin, W. S. Simultaneous Pell equations, 355 Bach, Eric, Lukes, Richard, Shallit, Jeffrey, and Williams, H. C. Results and estimates on pseu- dopowers, 1737 Bach, Eric, and Peralta, Ren´e. Asymptotic semismoothness probabilities , 1701 Bach, Eric, and Sorenson, Jonathan. Explicit bounds for primes in residue classes, 1717 Bhatia, Rajendra, and Li, Ren-Cang. On perturbations of matrix pencils with real spectra. II, 637 de Boor, Carl. On the Sauer-Xu formula for the error in multivariate polynomial interpolation, 1231 Borwein, Peter, and Erd´elyi,Tam´as. The integer Chebyshev problem, 661 Bosma, Wieb, and Stevenhagen, Peter. Density computations for real quadratic units, 1327 Bouchut, F., Bourdarias, Ch., and Perthame, B. A MUSCL method satisfying all the numerical entropy inequalities, 1439 Bourdarias, Ch. See Bouchut, F. Boyd, David W. On beta expansions for Pisot numbers, 841 . On the beta expansion for Salem numbers of degree 6, 861 Brenner, Susanne C. Two-level additive Schwarz preconditioners for nonconforming finite ele- ment methods, 897 Brezina, Marian. See Mandel, Jan Brown, Brienne E., and Gordon, Daniel M. On sequences without geometric progressions, 1749 Buchmann, Johannes, and Shoup, Victor. Constructing nonresidues in finite fields and the ex- tended Riemann hypothesis, 1311 Burthe, Ronald Joseph, Jr. Further investigations with the strong probable prime test, 373 Call, Gregory S., and Silverman, Joseph H. Computing the canonical height on K3 surfaces, 259 Carstensen, Carsten. Efficiency of a posteriori BEM–error estimates for first-kind integral equa- tions on quasi–uniform meshes, 69 Cheer, A. Y., and Goldston, D. A. Tur´an’s pure power sum problem, 1349 Chen, Goong. See Deng, Yuanhua Chen, Zhangxin, Ewing, Richard E., and Lazarov, Raytcho. Domain decomposition algorithms for mixed methods for second-order elliptic problems, 467 Chui, Charles K., and De Villiers, Johan M. Applications of optimally local interpolation to interpolatory approximants and compactly supported wavelets, 99 Chui, Charles K., and Hong, Dong. Construction of local C1 quartic spline elements for optimal- order approximation, 85 Clark, David A. Non-Galois cubic fields which are Euclidean but not norm-Euclidean, 1675 Cockburn, Bernardo, and Gremaud, Pierre-Alain. A priori error estimates for numerical meth- ods for scalar conservation laws. Part I: The general approach, 533 Cohen, Henri. Hermite and Smith normal form algorithms over Dedekind domains, 1681 Cohn, Harvey, and McKay, John. Spontaneous generation of modular invariants, 1295 Cools, Ronald, and Sloan, Ian H. Minimal cubature formulae of trigonometric degree, 1583 Coutsias, Evangelos A., Hagstrom, Thomas, and Torres, David. An efficient spectral method for ordinary differential equations with rational function coefficients, 611 Couture, Raymond, and L’Ecuyer, Pierre. Orbits and lattices for linear random number gener- ators with composite moduli , 189 Daberkow, M., and Pohst, M. On integral bases in relative quadratic extensions, 319 Deleglise, M., and Rivat, J. Computing π(x): the Meissel, Lehmer, Lagarias, Miller, Odlyzko method, 235 Demichelis, V. Quasi-interpolatory splines based on Schoenberg points, 1235 Deng, Yuanhua, Chen, Goong, Ni, Wei-Ming, and Zhou, Jianxin. Boundary element monotone iteration scheme for semilinear elliptic partial differential equations, 943 De Villiers, Johan M. See Chui, Charles K. Dimitrov, Dimitar K. Integration of polyharmonic functions, 1269 Doman, B. G. S. An asymptotic expansion for the incomplete beta function, 1283 Dubner, Harvey. Large Sophie Germain primes, 393 Duijvestijn, A. J. W. The number of polyhedral (3-connected planar) graphs, 1289 . Simple perfect squared squares and 2 × 1 squared rectangles of order 26, 1359 INDEX TO VOLUME 65 (1996)

Eichenauer-Herrmann, J¨urgen,and Emmerich, Frank. Compound inversive congruential pseu- dorandom numbers: an average-case analysis, 215 Ekl, Randy L. Equal sums of four seventh powers, 1755 Emmerich, Frank. See Eichenauer-Herrmann, J¨urgen . Pseudorandom vector generation by the compound inversive method, 749 Erd´elyi,Tam´as. See Borwein, Peter Erd˝os,P., and Lewin, Mordechai. d-complete sequences of integers, 837 Ewing, Richard E. See Chen, Zhangxin Farouki, R. T., and Goodman, T. N. T. On the optimal stability of the Bernstein basis, 1553 Flammang, V. Two new points in the spectrum of the absolute Mahler measure of totally positive algebraic integers, 307 French, Donald A., and Peterson, Todd E. A continuous space-time finite element method for the wave equation, 491 Fukuda, Takashi. Cyclotomic units and Greenberg’s conjecture for real quadratic fields, 1339 Fukuda, T., and Komatsu, K. A capitulation problem and Greenberg’s conjecture on real qua- dratic fields, 313 Ga´al,Istv´an. Computing all power integral bases in orders of totally real cyclic sextic number fields, 801 Gautschi, Walter, and Li, Shikang. On quadrature convergence of extended Lagrange interpola- tion, 1249 Gautschi, Walter, and Notaris, Sotirios E. Stieltjes polynomials and related quadrature formulae for a class of weight functions, 1257 Gayle, R. C., and Wolfe, J. M. Unicity in piecewise polynomial L1-approximation via an algo- rithm, 647 Goldston, D. A. See Cheer, A. Y. Goodman, T. N. T. See Farouki, R. T. Gordon, Daniel M. See Brown, Brienne E. Gori, Laura, and Micchelli, Charles A. On weight functions which admit explicit Gauss-Tur´an quadrature formulas, 1567 Gremaud, Pierre-Alain. See Cockburn, Bernardo Hagstrom, Thomas. See Coutsias, Evangelos A. Halpern, Laurence. Spectral methods in polar coordinates for the Stokes problem. Application to computation in unbounded domains, 507 Han, Wen Bao. The coefficients of primitive polynomials over finite fields, 331 Heinrich, S. Efficient algorithms for computing the L2-discrepancy, 1621 Hong, Dong. See Chui, Charles K. Indlekofer, Karl-Heinz, and J´arai,Antal. Largest known twin primes, 427 Iribarren, Gabriel. See Rivara, Mar´ıa-Cecilia J´arai,Antal. See Indlekofer, Karl-Heinz Jepsen, Charles H. Dissections of p : q rectangles, 771 Joe, Barry. See Liu, Anwei Joe, S. See Lyness, J. N. Kato, Takashi, Wu, Li-Ming, and Yanagihara, Niro. On a nonlinear congruential pseudorandom number generator, 227 . The serial test for a nonlinear pseudorandom number generator, 761 Keiper, J. B. On the zeros of the Ramanujan τ-Dirichlet series in the critical strip, 1613 Klouˇcek,Petr, Li, Bo, and Luskin, Mitchell. Analysis of a class of nonconforming finite elements for crystalline microstructures, 1111 Komatsu, K. See Fukuda, T. Kuijlaars, Arno B. J. The zeros of Faber polynomials generated by an m-star, 151 L’Ecuyer, Pierre. See Couture, Raymond . Maximally equidistributed combined Tausworthe generators, 203 Langtry, T. N. An application of diophantine approximation to the construction of rank-1 lattice quadrature rules, 1635 Laurie, Dirk P. Anti-Gaussian quadrature formulas, 739 Lawton, W., Lee, S. L., and Shen, Zuowei. An algorithm for matrix extension and wavelet con- struction, 723 Lazarov, Raytcho. See Chen, Zhangxin INDEX TO VOLUME 65 (1996)

L´ecot,Christian. Error bounds for quasi-Monte Carlo integration with nets, 179 Lee, S. L. See Lawton, W. Lewin, Mordechai. See Erd˝os,P. Li, Bo. See Klouˇcek,Petr Li, Ren-Cang. See Bhatia, Rajendra Li, Shikang. See Gautschi, Walter Li, T. Y., and Wang, Xiaoshen. The BKK root count in Cn, 1477 Liu, Anwei, and Joe, Barry. Quality local refinement of tetrahedral meshes based on 8-subtetrahedron subdivision, 1183 Liu, Hailiang, and Wang, Jinghua. Nonlinear stability of stationary discrete shocks for nonconvex scalar conservation laws, 1137 L¨oh,G¨unter, and Niebuhr, Wolfgang. A new algorithm for constructing large Carmichael num- bers, 823 Lubich, Ch., Sloan, I. H., and Thom´ee,V. Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term, 1 Lukes, R. F., Patterson, C. D., and Williams, H. C. Some results on pseudosquares, 361 Lukes, Richard. See Bach, Eric Luskin, Mitchell. See Klouˇcek,Petr Lyness, J. N., and Joe, S. Triangular canonical forms for lattice rules of prime-power order, 165 Malmliden, Johan F., and Petersson, N. Anders. A fast iterative method to compute the flow around a submerged body, 1067 Malta, Iaci, Saldanha, Nicolau C., and Tomei, Carlos. The numerical inversion of functions from the plane to the plane, 1531 Mandel, Jan, and Brezina, Marian. Balancing domain decomposition for problems with large jumps in coefficients, 1387 von Matt, Urs, and Stewart, G. W. Rounding errors in solving block Hessenberg systems, 115 McKay, John. See Cohn, Harvey Micchelli, Charles A. See Gori, Laura Mignotte, Maurice, Peth¨o,Attila, and Roth, Ralf. Complete solutions of a family of quartic Thue and index form equations, 341 Morgan, Ronald B. On restarting the Arnoldi method for large nonsymmetric eigenvalue prob- lems, 1213 Nessyahu, Haim. Convergence rate of approximate solutions to weakly coupled nonlinear sys- tems, 575 Ni, Wei-Ming. See Deng, Yuanhua Nicolaides, R. A., and Wu, X. Analysis and convergence of the MAC scheme. II. Navier-Stokes equations, 29 Niebuhr, Wolfgang. See L¨oh,G¨unter Noelle, Sebastian. A note on entropy inequalities and error estimates for higher-order accurate finite volume schemes on irregular families of grids, 1155 Notaris, Sotirios E. See Gautschi, Walter Oswald, Peter. Preconditioners for nonconforming discretizations, 923 Palamara Orsi, Annamaria. Product integration for Volterra integral equations of the second kind with weakly singular kernels, 1201 Papageorgiou, G. See Papakostas, S. N. Papakostas, S. N., and Papageorgiou, G. A family of fifth-order Runge-Kutta pairs, 1165 Patterson, C. D. See Lukes, R. F. Pearson, Kimberly. Integral cohomology and detection of w-basic 2-groups, 291 Peralta, Ren´e. See Bach, Eric Perthame, B. See Bouchut, F. Peszy´nska, Ma lgorzata. Finite element approximation of diffusion equations with convolution terms, 1019 Peterson, Todd E. See French, Donald A. Petersson, N. Anders. See Malmliden, Johan F. Peth¨o,Attila. See Mignotte, Maurice Pohst, M. See Daberkow, M. Quak, Ewald. Trigonometric wavelets for Hermite interpolation, 683 Ramar´e,Olivier, and Rumely, Robert. Primes in arithmetic progressions, 397 INDEX TO VOLUME 65 (1996)

Rivara, Mar´ıa-Cecilia,and Iribarren, Gabriel. The 4-triangles longest-side partition of triangles and linear refinement algorithms, 1485 Rivat, J. See Deleglise, M. Rodr´ıguez,Rodolfo, and Solomin, Jorge E. The order of convergence of eigenfrequencies in finite element approximations of fluid-structure interaction problems, 1463 Ron, Amos, and Sun, Xingping. Strictly positive definite functions on spheres in euclidean spaces, 1513 Roth, Ralf. See Mignotte, Maurice Rumely, Robert. See Ramar´e,Olivier Rump, S. M. Expansion and estimation of the range of nonlinear functions, 1503 Rusten, Torgeir, Vassilevski, Panayot S., and Winther, Ragnar. Interior penalty preconditioners for mixed finite element approximations of elliptic problems, 447 Saldanha, Nicolau C. See Malta, Iaci Schatz, Alfred H., and Wang, Junping. Some new error estimates for Ritz–Galerkin methods with minimal regularity assumptions, 19 Schwab, Christoph, and Suri, Manil. The p and hp versions of the finite element method for problems with boundary layers, 1403 Shallit, Jeffrey. See Bach, Eric Shen, Jie. On error estimates of the projection methods for the Navier-Stokes equations: Second- order schemes, 1039 Shen, Zuowei. See Lawton, W. Shoup, Victor. See Buchmann, Johannes Silverman, Joseph H. See Call, Gregory S. Sloan, I. H. See Lubich, Ch. Sloan, Ian H. See Cools, Ronald Smith, David M. A multiple-precision division algorithm, 157 Solomin, Jorge E. See Rodr´ıguez,Rodolfo Sorenson, Jonathan. See Bach, Eric Stevenhagen, Peter. See Bosma, Wieb Stevenson, Rob. The frequency decomposition multilevel method: A robust additive hierarchical basis preconditioner, 983 Stewart, G. W. See von Matt, Urs Strela, V. V., and Tyrtyshnikov, E. E. Which circulant preconditioner is better?, 137 Stynes, Martin. See Sun, Guangfu Sun, Guangfu, and Stynes, Martin. A uniformly convergent method for a singularly perturbed semilinear reaction–diffusion problem with multiple solutions, 1085 Sun, Xingping. See Ron, Amos Suri, Manil. See Schwab, Christoph Taya, Hisao. Computation of Z3-invariants of real quadratic fields, 779 Thom´ee,V. See Lubich, Ch. Tomei, Carlos. See Malta, Iaci Torres, David. See Coutsias, Evangelos A. Tyrtyshnikov, E. E. See Strela, V. V. Urabe, Tohsuke. Calculation of Manin’s invariant for Del Pezzo surfaces, 247 Van Keer, R. See Vanmaele, M. Vanmaele, M., and Van Keer, R. On a variational approximation method for a class of elliptic eigenvalue problems in composite structures, 999 Vassilevski, Panayot S. See Rusten, Torgeir Wagner, Christian. Class number 5, 6 and 7, 785 Wagstaff, Samuel S., Jr. Aurifeuillian factorizations and the period of the Bell numbers modulo a prime, 383 Wang, Jinghua. See Liu, Hailiang Wang, Junping. See Schatz, Alfred H. Wang, Xiaoshen. See Li, T. Y. Williams, H. C. See Lukes, R. F. . See Bach, Eric Winther, Ragnar. See Rusten, Torgeir Wolfe, J. M. See Gayle, R. C. INDEX TO VOLUME 65 (1996)

Wu, Li-Ming. See Kato, Takashi . See Kato, Takashi Wu, X. See Nicolaides, R. A. Xu, Yuesheng, and Zhao, Yunhe. An extrapolation method for a class of boundary integral equa- tions, 587 Xu, Yu-lin. Fast evaluation of the Gaunt coefficients, 1601 Yanagihara, Niro. See Kato, Takashi . See Kato, Takashi Yang, Huanan. On wavewise entropy inequalities for high-resolution schemes. I: The semidis- crete case, 45 Zhang, Zhimin. Ultraconvergence of the patch recovery technique, 1431 Zhao, Yunhe. See Xu, Yuesheng Zhou, Jianxin. See Deng, Yuanhua INDEX OF REVIEWS BY AUTHOR OF WORK REVIEWED

Review Author Number Classification Page

Abell, Martha L., & 18 68-01, 68Q40 881 Braselton, James P. Abell, Martha L., & 46 00A20, 68Q40 1764 Braselton, James P. Anderson, E., Bai, Z., 45 65F05, 65F15, 65F20, 65F35, 65Y05, Bischof, C., Demmel, J., 65Y20, 65Y99 1763 Dongarra, J., du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Ostrouchov, S., & Sorensen, D. Axelsson, Owe 21 65-02, 65F05, 65F10 886 Bai, Z. 45 See Anderson, E. 1757 Bailey, David H., 12 65-06, 65Y05 440 Bjørstad, Petter E., Gilbert, John R., Mascagni, Michael V., Schreiber, Robert S., Simon, Horst D., Torczon, Virginia J., & Watson, Layne T. (Editors) 2 See Lions, J.-L. 430 Banks, H. T. (Editor) 3 49-02, 70-08, 70Q05 430 Bini, Dario, & Pan, Victor Y. 22 15A06, 65F05, 68Q25 888 Bischof, C. 45 See Anderson, E. 1763 12 See Bailey, David H. 440 Braselton, James P. 18 See Abell, Martha L. 881 Braselton, James P. 46 See Abell, Martha L. 1764 Brenner, Susanne C., & 14 65-01, 65N30, 65N55, 73Cxx 877 Scott, L. Ridgway Briggs, William L., & 33 39A05, 44A12, 65T10, 94A12 1371 Henson, Van Emden Brown, J. David, 6 01A70, 65-06, 65F10, 65T20, 76W05, 83-06, Chu, Moody T., 83C05, 85-06 432 Ellison, Donald C., & Plemmons, Robert J. (Editors) Butuzov, Valentin F. 30 See Vasil′eva, Adelaida B. 1366 6 See Brown, J. David 432 Chui, Charles K., 24 41-06, 41A30, 41A99, 65-06 890 Montefusco, Laura, & Puccio, Luigia (Editors) Ciarlet, P. G., & Lions, J. L. 1 65-00, 41-00, 41A05, 41A21, 41A55, 41A65, (Editors) 65C05, 65H05, 65T20, 73C50, 73V20 429 Ciarlet, Philippe G., 40 73-06, 73K05, 73K10, 73K15, 73V25 1760 Trabucho, Lu´ıs, & Viano,˜ Juan M. (Editors) Cohen, Gary (Editor) 31 65-06, 76-06, 78-06, 35L05, 65C20 1369 INDEX OF REVIEWS BY AUTHOR OF WORK REVIEWED

Cohen, Henri 13 11-01, 11Yxx 440 Coombes, Kevin R., 32 34-01, 34-04 1369 Hunt, Brian R., Lipsman, Ronald L., Osborn, John E., & Stuck, Garrett J. Cox, Earl 4 94-01, 94D05 431 du Croz, J. 45 See Anderson, E. 1763 Demmel, J. 45 See Anderson, E. 1763 Deuflhard, Peter, & 38 65-01, 65Bxx, 65Cxx, 65Dxx, 65Fxx, Hohmann, Andreas 65Gxx 1757 Dikshit, H. P., & 5 41-06, 65-06, 42-06, 46-06 432 Micchelli, C. A. (Editors) Dongarra, J. 45 See Anderson, E. 1763 Dongarra, Jack J., & 16 65-06, 65Y05 879 Tourancheau, Bernard (Editors) 6 See Brown, J. David 432 Farin, Gerald E. 25 65-01, 65D07, 65Y25, 68U07 891 Fiume, Eugene 43 65-01, 68-01, 68U05 1761 Foufoula-Georgiou, Efi, & 9 42-06, 42C10, 86-06, 86-08 436 Kumar, Praveen (Editors) Friedman, Avner, & 15 00A69, 34-01, 35-01, 65-01 878 Littman, Walter Gander, Walter, & 17 68-01, 65-01 880 Hrebˇ ´ıcek,ˇ Jirˇ´ı 12 See Bailey, David H. 440 Greenbaum, A. 45 See Anderson, E. 1763 Hammarling, S. 45 See Anderson, E. 1763 Henson, Van Emden 33 See Briggs, William L. 1371 Hohmann, Andreas 38 See Deuflhard, Peter 1757 Hrebˇ ´ıcek,ˇ Jirˇ´ı 17 See Gander, Walter 880 Hunt, Brian R. 32 See Coombes, Kevin R. 1369 Kalachev, Leonid V. 30 See Vasil′eva, Adelaida B. 1366 Krishna, Bal 27 See Krishna, Hari 893 Krishna, Hari, Krishna, Bal, 27 12Y05, 65T10, 94B05 893 Lin, Kuo-Yu, & Sun, Jenn-Dong Krˇ´ıˇzek, M., Neittaanmaki,¨ P., 29 65-06, 65M60, 65N30 1365 & Stenberg, R. (Editors) 9 See Foufoula-Georgiou, Efi 436 Lau, H. T. 34 65-00, 65-04 1371 Laurent, Pierre-Jean, 7 41-06, 41A15, 65-06, 65D07, 65D10 435 le Mehaut´ e,´ Alain, & Schumaker, Larry L. (Editors) Lidl, Rudolf, & 36 11Txx, 94A60, 94B60 1376 Niederreiter, Harald INDEX OF REVIEWS BY AUTHOR OF WORK REVIEWED

Lin, Kuo-Yu 27 See Krishna, Hari 893 1 See Ciarlet, P. G. 429 Lions, J.-L., & Baiocchi, C. 2 65-06, 65Nxx 430 (Editors) Lipsman, Ronald L. 32 See Coombes, Kevin R. 1369 Littman, Walter 15 See Friedman, Avner 878 Mangasarian, Olvi L. 19 49-02, 49K40, 65K05 884 12 See Bailey, David H. 440 McKenney, A. 45 See Anderson, E. 1763 7 See Laurent, Pierre-Jean 435 5 See Dikshit, H. P. 432 Micchelli, Charles A. 23 65-02, 65D17 889 Milovanovic,´ G. V., 10 41-02, 41A17, 26C05, 26C10, 26Dxx 438 Mitrinovic,´ D. S., & Rassias, Th. M. Mitrinovic,´ D. S. 10 See Milovanovic,´ G. V. 438 Molenaar, J. 39 65N30, 65N50, 65N55, 82D99 1758 24 See Chui, Charles K. 890 29 See Krˇ´ıˇzek, M. 1365 Nemirovskii, Arkadii 20 See Nesterov, Yurii 884 Nesterov, Yurii, & 20 49-02, 49M35, 49M45, 65K05 884 Nemirovskii, Arkadii Niederreiter, Harald 36 See Lidl, Rudolf 1376 Osborn, John E. 32 See Coombes, Kevin R. 1369 Ostrouchov, S. 45 See Anderson, E. 1763 Pan, Victor Y. 22 See Bini, Dario 888 6 See Brown, J. David 432 Plis, Alexander I. 41 See Shikin, Eugene V. 1760 Ploufee, Simon 28 See Sloane, N. J. A. 894 24 See Chui, Charles K. 890 Rassias, Th. M. 10 See Milovanovic,´ G. V. 438 Riesel, Hans 37 11-02, 11Y05, 11Y11, 11Y16, 11Y35, 11Y40 1377 Rubio, J. E. 11 49-02, 49J10, 65K10 439 Sabot, Gary W. (Editor) 44 65-02, 65Yxx 1763 Sapidis, Nickolas S. (Editor) 26 65-06, 65D05, 65D07, 65D17 892 12 See Bailey, David H. 440 7 See Laurent, Pierre-Jean 435 Scott, L. Ridgway 14 See Brenner, Susanne C. 877 Shikin, Eugene V., & 41 65-00, 65-04, 41-00, 41-04, 41A15 1760 Plis, Alexander I. 12 See Bailey, David H. 440 Sloane, N. J. A., & 28 11-00, 11B83 894 Ploufee, Simon INDEX OF REVIEWS BY AUTHOR OF WORK REVIEWED

Sobol′, Ilya M. 42 65-01, 65C05, 65C10 1761 Sorensen, D. 45 See Anderson, E. 1763 29 See Krˇ´ıˇzek, M. 1365 Stepanov, Serguei A. 47 11-02, 11Gxx 1767 Stuck, Garrett J. 32 See Coombes, Kevin R. 1369 Sun, Jenn-Dong 27 See Krishna, Hari 893 12 See Bailey, David H. 440 16 See Dongarra, Jack J. 879 40 See Ciarlet, Philippe G. 1760 Vasil′eva, Adelaida B., 30 34E15, 35B25, 73U05, 78A30, 80A25, Butuzov, Valentin F., & 92C20 1366 Kalachev, Leonid V. 40 See Ciarlet, Philippe G. 1760 12 See Bailey, David H. 440 Wickerhauser, Mladen Victor 8 41-04, 41A30, 42A38, 65D99, 68U10 436 Zahar, R. V. M. (Editor) 35 01A70, 33-XX, 33C45, 41-XX, 41A55 1372

INDEX OF REVIEWS BY SUBJECT OF WORK REVIEWED

Review Author Number Title Page

00-XX General 00A20 Dictionaries and other general reference works Abell, Martha L., & 46 The Maple V handbook 1764 Braselton, James P. 00A69 General applied mathematics Friedman, Avner, & 15 Industrial mathematics: A course in solving Littman, Walter real-world problems 878 01-XX History and biography 01A70 Biographies, obituaries, personalia, bibliographies Brown, J. David, 6 Proceedings of the Cornelius Lanczos Chu, Moody T., international centenary conference 432 Ellison, Donald C., & Plemmons, Robert J. (Editors) Zahar, R. V. M. (Editor) 35 Approximation and computation: A festschrift in honor of Walter Gautschi 1372 11-XX Number theory 11-00 General reference works Sloane, N. J. A., & 28 The encyclopedia of integer sequences 894 Ploufee, Simon 11-01 Instructional exposition Cohen, Henri 13 A course in computational algebraic number theory 440 INDEX OF REVIEWS BY SUBJECT OF WORK REVIEWED

11-02 Research exposition Riesel, Hans 37 Prime numbers and computer methods for factorization 1377 Stepanov, Serguei A. 47 Arithmetic of algebraic curves 1767

11B83 Special sequences and polynomials Sloane, N. J. A., & 28 The encyclopedia of integer sequences 894 Ploufee, Simon

11Gxx Arithmetic algebraic geometry Stepanov, Serguei A. 47 Arithmetic of algebraic curves 1767

11Txx Finite fields and commutative rings Lidl, Rudolf, & 36 Introduction to finite fields and their Niederreiter, Harald applications 1376

11Yxx Computational number theory Cohen, Henri 13 A course in computational algebraic number theory 440

11Y05 Factorization Riesel, Hans 37 Prime numbers and computer methods for factorization 1377 11Y11 Primality Riesel, Hans 37 Prime numbers and computer methods for factorization 1377 11Y16 Algorithms; complexity Riesel, Hans 37 Prime numbers and computer methods for factorization 1377 11Y35 Analytic computations Riesel, Hans 37 Prime numbers and computer methods for factorization 1377 11Y40 Algebraic number theory computations Riesel, Hans 37 Prime numbers and computer methods for factorization 1377 12-XX Field theory and polynomials 12Y05 Computational aspects of field theory and polynomials Krishna, Hari, Krishna, Bal, 27 Computational number theory and digital Lin, Kuo-Yu, & signal processing: Fast algorithms and Sun, Jenn-Dong error control techniques 893 15-XX Linear and multilinear algebra; matrix theory 15A06 Linear equations Bini, Dario, & Pan, Victor Y. 22 Polynomial and matrix computations: Fun- damental algorithms, Vol. 1 888 26-XX Real functions 26C05 Polynomials: analytic properties, etc. Milovanovic,´ G. V., 10 Topics in polynomials: extremal problems, Mitrinovic,´ D. S., & inequalities, zeros 438 Rassias, Th. M. INDEX OF REVIEWS BY SUBJECT OF WORK REVIEWED

26C10 Polynomials: location of zeros Milovanovic,´ G. V., 10 Topics in polynomials: extremal problems, Mitrinovic,´ D. S., & inequalities, zeros 438 Rassias, Th. M. 26Dxx Inequalities Milovanovic,´ G. V., 10 Topics in polynomials: extremal problems, Mitrinovic,´ D. S., & inequalities, zeros 438 Rassias, Th. M. 33-XX Special functions Zahar, R. V. M. (Editor) 35 Approximation and computation: A festschrift in honor of Walter Gautschi 1372 33C45 Orthogonal polynomials and functions Zahar, R. V. M. (Editor) 35 Approximation and computation: A festschrift in honor of Walter Gautschi 1372 34-XX Ordinary differential equations 34-01 Instructional exposition Coombes, Kevin R., 32 Differential equations with Mathematica 1369 Hunt, Brian R., Lipsman, Ronald L., Osborn, John E., & Stuck, Garrett J. Friedman, Avner, & 15 Industrial mathematics: A course in solving Littman, Walter real-world problems 878 34-04 Explicit machine computation and programs Coombes, Kevin R., 32 Differential equations with Mathematica 1369 Hunt, Brian R., Lipsman, Ronald L., Osborn, John E., & Stuck, Garrett J. 34E15 Singular perturbations, general theory Vasil′eva, Adelaida B., 30 The boundary function method for singular Butuzov, Valentin F., & perturbation problems 1366 Kalachev, Leonid V. 35-XX Partial differential equations 35-01 Instructional exposition Friedman, Avner, & 15 Industrial mathematics: A course in solving Littman, Walter real-world problems 878 35B25 Singular perturbations Vasil′eva, Adelaida B., 30 The boundary function method for singular Butuzov, Valentin F., & perturbation problems 1366 Kalachev, Leonid V. 35L05 Wave equation Cohen, Gary (Editor) 31 Mathematical and numerical aspects of wave propagation 1369 39-XX Finite differences and functional equations 39A05 General Briggs, William L., & 33 The DFT: An owner’s manual for the Henson, Van Emden discrete Fourier transform 1371 INDEX OF REVIEWS BY SUBJECT OF WORK REVIEWED

41-XX Approximations and expansions Zahar, R. V. M. (Editor) 35 Approximation and computation: A festschrift in honor of Walter Gautschi 1372 41-00 General reference works Ciarlet, P. G., & Lions, J. L. 1 Handbook of numerical analysis 429 (Editors) Shikin, Eugene V., & 41 Handbook on splines for the user 1760 Plis, Alexander I. 41-02 Research exposition Milovanovic,´ G. V., 10 Topics in polynomials: extremal problems, Mitrinovic,´ D. S., & inequalities, zeros 438 Rassias, Th. M. 41-04 Explicit machine computation and programs Shikin, Eugene V., & 41 Handbook on splines for the user 1760 Plis, Alexander I. Wickerhauser, Mladen Victor 8 Adapted wavelet analysis from theory to software 436 41-06 Proceedings, conferences, collections, etc. Chui, Charles K., 24 Wavelets: theory, algorithms, and applica- Montefusco, Laura, & tions 890 Puccio, Luigia (Editors) Dikshit, H. P., & 5 Advances in computational mathematics: Micchelli, C. A. (Editors) New Delhi, India 432 Laurent, Pierre-Jean, 7 Curves and surfaces in geometric design 435 le Mehaut´ e,´ Alain, & Schumaker, Larry L. (Editors) 41A05 Interpolation Ciarlet, P. G., & Lions, J. L. 1 Handbook of numerical analysis 429 (Editors) 41A15 Spline approximation Laurent, Pierre-Jean, 7 Curves and surfaces in geometric design 435 le Mehaut´ e,´ Alain, & Schumaker, Larry L. (Editors) Shikin, Eugene V., & 41 Handbook on splines for the user 1760 Plis, Alexander I. 41A17 Inequalities in approximation Milovanovic,´ G. V., 10 Topics in polynomials: extremal problems, Mitrinovic,´ D. S., & inequalities, zeros 438 Rassias, Th. M. 41A21 Pad´eapproximation Ciarlet, P. G., & Lions, J. L. 1 Handbook of numerical analysis 429 (Editors) 41A30 Approximation by other special function classes Chui, Charles K., 24 Wavelets: theory, algorithms, and applica- Montefusco, Laura, & tions 890 Puccio, Luigia (Editors) INDEX OF REVIEWS BY SUBJECT OF WORK REVIEWED

Wickerhauser, Mladen Victor 8 Adapted wavelet analysis from theory to software 436 41A55 Approximate quadratures Ciarlet, P. G., & Lions, J. L. 1 Handbook of numerical analysis 429 (Editors) Zahar, R. V. M. (Editor) 35 Approximation and computation: A festschrift in honor of Walter Gautschi 1372 41A65 Abstract approximation theory Ciarlet, P. G., & Lions, J. L. 1 Handbook of numerical analysis 429 (Editors)

41A99 Miscellaneous topics Chui, Charles K., 24 Wavelets: theory, algorithms, and applica- Montefusco, Laura, & tions 890 Puccio, Luigia (Editors)

42-XX Fourier analysis 42-06 Proceedings, conferences, collections, etc. Dikshit, H. P., & 5 Advances in computational mathematics: Micchelli, C. A. (Editors) New Delhi, India 432 Foufoula-Georgiou, Efi, & 9 Wavelets in geophysics 436 Kumar, Praveen (Editors)

42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type Wickerhauser, Mladen Victor 8 Adapted wavelet analysis from theory to software 436 42C10 Fourier series in special orthogonal functions Foufoula-Georgiou, Efi, & 9 Wavelets in geophysics 436 Kumar, Praveen (Editors)

44-XX Integral transforms, operational calculus 44A12 Radon transform Briggs, William L., & 33 The DFT: An owner’s manual for the Henson, Van Emden discrete Fourier transform 1371 46-XX Functional analysis 46-06 Proceedings, conferences, collections, etc. Dikshit, H. P., & 5 Advances in computational mathematics: Micchelli, C. A. (Editors) New Delhi, India 432

49-XX Calculus of variations and optimal control; optimization 49-02 Research exposition Banks, H. T. (Editor) 3 Control and estimation in distributed parameter systems 430 Mangasarian, Olvi L. 19 Nonlinear programming 884 Nesterov, Yurii, & 20 Interior-point polynomial algorithms in Nemirovskii, Arkadii convex programming 884 Rubio, J. E. 11 Optimization and nonstandard analysis 439

49J10 Free problems in two or more independent variables Rubio, J. E. 11 Optimization and nonstandard analysis 439 INDEX OF REVIEWS BY SUBJECT OF WORK REVIEWED

49K40 Sensitivity of optimal solutions in the presence of perturbations

Mangasarian, Olvi L. 19 Nonlinear programming 884

49M35 Methods of linear programming type

Nesterov, Yurii, & 20 Interior-point polynomial algorithms in Nemirovskii, Arkadii convex programming 884

49M45 Methods of convex programming type

Nesterov, Yurii, & 20 Interior-point polynomial algorithms in Nemirovskii, Arkadii convex programming 884

65-XX Numerical analysis 65-00 General reference works

Ciarlet, P. G., & Lions, J. L. 1 Handbook of numerical analysis 429 (Editors) Lau, H. T. 34 A numerical library in C for scientists and engineers 1371 Shikin, Eugene V., & 41 Handbook on splines for the user 1760 Plis, Alexander I.

65-01 Instructional exposition

Brenner, Susanne C., & 14 The mathematical theory of finite element Scott, L. Ridgway methods 877 Deuflhard, Peter, & 38 Numerical analysis: A first course in Hohmann, Andreas scientific computation 1757 Farin, Gerald E. 25 NURB curves and surfaces: from projective geometry to practical use 891 Fiume, Eugene 43 An introduction to scientific, symbolic, and graphical computation 1761 Friedman, Avner, & 15 Industrial mathematics: A course in solving Littman, Walter real-world problems 878 Gander, Walter, & 17 Solving problems in scientific computing Hrebˇ ´ıcek,ˇ Jirˇ´ı using MAPLE and MATLAB 880 Sobol′, Ilya M. 42 A primer for the Monte Carlo method 1761

65-02 Research exposition

Axelsson, Owe 21 Iterative solution methods 886

Micchelli, Charles A. 23 Mathematical aspects of geometrical mod- eling 889 Sabot, Gary W. (Editor) 44 High performance computing—Problem solving with parallel and vector archi- tectures 1763

65-04 Explicit machine computation and programs

Lau, H. T. 34 A numerical library in C for scientists and engineers 1371 Shikin, Eugene V., & 41 Handbook on splines for the user 1760 Plis, Alexander I. INDEX OF REVIEWS BY SUBJECT OF WORK REVIEWED

65-06 Proceedings, conferences, collections, etc. Bailey, David H., 12 Parallel processing for scientific comput- Bjørstad, Petter E., ing 440 Gilbert, John R., Mascagni, Michael V., Schreiber, Robert S., Simon, Horst D., Torczon, Virginia J., & Watson, Layne T. (Editors) Brown, J. David, 6 Proceedings of the Cornelius Lanczos Chu, Moody T., international centenary conference 432 Ellison, Donald C., & Plemmons, Robert J. (Editors) Chui, Charles K., 24 Wavelets: theory, algorithms, and applica- Montefusco, Laura, & tions 890 Puccio, Luigia (Editors) Cohen, Gary (Editor) 31 Mathematical and numerical aspects of wave propagation 1369 Dikshit, H. P., & 5 Advances in computational mathematics: Micchelli, C. A. (Editors) New Delhi, India 432 Dongarra, Jack J., & 16 Environments and tools for parallel scien- Tourancheau, Bernard tific computing 879 (Editors) Krˇ´ıˇzek, M., Neittaanmaki,¨ P., 29 Finite element methods: Fifty years of the & Stenberg, R. (Editors) Courant element 1365 Laurent, Pierre-Jean, 7 Curves and surfaces in geometric design 435 le Mehaut´ e,´ Alain, & Schumaker, Larry L. (Editors) Lions, J.-L., & Baiocchi, C. 2 Boundary value problems for partial differ- (Editors) ential equations and applications 430 Sapidis, Nickolas S. (Editor) 26 Designing fair curves and surfaces 892

65Bxx Acceleration of convergence Deuflhard, Peter, & 38 Numerical analysis: A first course in Hohmann, Andreas scientific computation 1757

65Cxx Numerical simulation Deuflhard, Peter, & 38 Numerical analysis: A first course in Hohmann, Andreas scientific computation 1757

65C05 Monte Carlo methods Ciarlet, P. G., & Lions, J. L. 1 Handbook of numerical analysis 429 (Editors) Sobol′, Ilya M. 42 A primer for the Monte Carlo method 1761

65C10 Random number generation Sobol′, Ilya M. 42 A primer for the Monte Carlo method 1761

65C20 Models, numerical methods Cohen, Gary (Editor) 31 Mathematical and numerical aspects of wave propagation 1369 INDEX OF REVIEWS BY SUBJECT OF WORK REVIEWED

65Dxx Numerical approximation Deuflhard, Peter, & 38 Numerical analysis: A first course in Hohmann, Andreas scientific computation 1757

65D05 Interpolation Sapidis, Nickolas S. (Editor) 26 Designing fair curves and surfaces 892

65D07 Splines Farin, Gerald E. 25 NURB curves and surfaces: from projective geometry to practical use 891 Laurent, Pierre-Jean, 7 Curves and surfaces in geometric design 435 le Mehaut´ e,´ Alain, & Schumaker, Larry L. (Editors) Sapidis, Nickolas S. (Editor) 26 Designing fair curves and surfaces 892

65D10 Smoothing, curve fitting Laurent, Pierre-Jean, 7 Curves and surfaces in geometric design 435 le Mehaut´ e,´ Alain, & Schumaker, Larry L. (Editors)

65D17 Computer aided design Micchelli, Charles A. 23 Mathematical aspects of geometrical mod- eling 889 Sapidis, Nickolas S. (Editor) 26 Designing fair curves and surfaces 892

65D99 None of the above, but in this section Wickerhauser, Mladen Victor 8 Adapted wavelet analysis from theory to software 436 65Fxx Numerical linear algebra Deuflhard, Peter, & 38 Numerical analysis: A first course in Hohmann, Andreas scientific computation 1757

65F05 Direct methods for linear systems and matrix inversion Anderson, E., Bai, Z., 45 LAPACK users’ guide 1763 Bischof, C., Demmel, J., Dongarra, J., du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Ostrouchov, S., & Sorensen, D. Axelsson, Owe 21 Iterative solution methods 886 Bini, Dario, & Pan, Victor Y. 22 Polynomial and matrix computations: Fun- damental algorithms, Vol. 1 888

65F10 Iterative methods for linear systems Axelsson, Owe 21 Iterative solution methods 886 Brown, J. David, 6 Proceedings of the Cornelius Lanczos Chu, Moody T., international centenary conference 432 Ellison, Donald C., & Plemmons, Robert J. (Editors) INDEX OF REVIEWS BY SUBJECT OF WORK REVIEWED

65F15 Eigenvalues, eigenvectors Anderson, E., Bai, Z., 45 LAPACK users’ guide 1763 Bischof, C., Demmel, J., Dongarra, J., du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Ostrouchov, S., & Sorensen, D. 65F20 Overdetermined systems, pseudoinverses Anderson, E., Bai, Z., 45 LAPACK users’ guide 1763 Bischof, C., Demmel, J., Dongarra, J., du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Ostrouchov, S., & Sorensen, D. 65F35 Matrix norms, conditioning, scaling Anderson, E., Bai, Z., 45 LAPACK users’ guide 1763 Bischof, C., Demmel, J., Dongarra, J., du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Ostrouchov, S., & Sorensen, D. 65Gxx Error analysis Deuflhard, Peter, & 38 Numerical analysis: A first course in Hohmann, Andreas scientific computation 1757 65H05 Single equations Ciarlet, P. G., & Lions, J. L. 1 Handbook of numerical analysis 429 (Editors)

65K05 Mathematical programming Mangasarian, Olvi L. 19 Nonlinear programming 884 Nesterov, Yurii, & 20 Interior-point polynomial algorithms in Nemirovskii, Arkadii convex programming 884 65K10 Optimization and variational techniques Rubio, J. E. 11 Optimization and nonstandard analysis 439 65M60 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods Krˇ´ıˇzek, M., Neittaanmaki,¨ P., 29 Finite element methods: Fifty years of the & Stenberg, R. (Editors) Courant element 1365

65Nxx Partial differential equations, boundary value problems Lions, J.-L., & Baiocchi, C. 2 Boundary value problems for partial differ- (Editors) ential equations and applications 430

65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods Brenner, Susanne C., & 14 The mathematical theory of finite element Scott, L. Ridgway methods 877 INDEX OF REVIEWS BY SUBJECT OF WORK REVIEWED

Krˇ´ıˇzek, M., Neittaanmaki,¨ P., 29 Finite element methods: Fifty years of the & Stenberg, R. (Editors) Courant element 1365 Molenaar, J. 39 Multigrid methods for semiconductor device simulation 1758 65N50 Mesh generation and refinement Molenaar, J. 39 Multigrid methods for semiconductor device simulation 1758 65N55 Multigrid methods; domain decomposition Brenner, Susanne C., & 14 The mathematical theory of finite element Scott, L. Ridgway methods 877 Molenaar, J. 39 Multigrid methods for semiconductor device simulation 1758 65T10 Trigonometric approximation and interpolation Briggs, William L., & 33 The DFT: An owner’s manual for the Henson, Van Emden discrete Fourier transform 1371 Krishna, Hari, Krishna, Bal, 27 Computational number theory and digital Lin, Kuo-Yu, & signal processing: Fast algorithms and Sun, Jenn-Dong error control techniques 893

65T20 Discrete and fast Fourier transforms Brown, J. David, 6 Proceedings of the Cornelius Lanczos Chu, Moody T., international centenary conference 432 Ellison, Donald C., & Plemmons, Robert J. (Editors) Ciarlet, P. G., & Lions, J. L. 1 Handbook of numerical analysis 429 (Editors)

65Yxx Computer aspects of numerical algorithms Sabot, Gary W. (Editor) 44 High performance computing—Problem solving with parallel and vector archi- tectures 1763 65Y05 Parallel computation Anderson, E., Bai, Z., 45 LAPACK users’ guide 1763 Bischof, C., Demmel, J., Dongarra, J., du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Ostrouchov, S., & Sorensen, D. Bailey, David H., 12 Parallel processing for scientific comput- Bjørstad, Petter E., ing 440 Gilbert, John R., Mascagni, Michael V., Schreiber, Robert S., Simon, Horst D., Torczon, Virginia J., & Watson, Layne T. (Editors) Dongarra, Jack J., & 16 Environments and tools for parallel scien- Tourancheau, Bernard tific computing 879 (Editors) INDEX OF REVIEWS BY SUBJECT OF WORK REVIEWED

65Y20 Complexity and performance of numerical algorithms

Anderson, E., Bai, Z., 45 LAPACK users’ guide 1763 Bischof, C., Demmel, J., Dongarra, J., du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Ostrouchov, S., & Sorensen, D.

65Y25 Computer graphics and computational geometry

Farin, Gerald E. 25 NURB curves and surfaces: from projective geometry to practical use 891

65Y99 None of the above, but in this section

Anderson, E., Bai, Z., 45 LAPACK users’ guide 1763 Bischof, C., Demmel, J., Dongarra, J., du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Ostrouchov, S., & Sorensen, D.

68-XX Computer science 68-01 Instructional exposition

Abell, Martha L., & 18 Maple V by example 881 Braselton, James P. Fiume, Eugene 43 An introduction to scientific, symbolic, and graphical computation 1761 Gander, Walter, & 17 Solving problems in scientific computing Hrebˇ ´ıcek,ˇ Jirˇ´ı using MAPLE and MATLAB 880

68Q25 Analysis of algorithms and problem complexity

Bini, Dario, & Pan, Victor Y. 22 Polynomial and matrix computations: Fun- damental algorithms, Vol. 1 888

68Q40 Symbolic computation, algebraic computation

Abell, Martha L., & 18 Maple V by example 881 Braselton, James P. Abell, Martha L., & 46 The Maple V handbook 1764 Braselton, James P.

68U05 Computer graphics; computational geometry

Fiume, Eugene 43 An introduction to scientific, symbolic, and graphical computation 1761

68U07 Computer-aided design

Farin, Gerald E. 25 NURB curves and surfaces: from projective geometry to practical use 891

68U10 Image processing

Wickerhauser, Mladen Victor 8 Adapted wavelet analysis from theory to software 436 INDEX OF REVIEWS BY SUBJECT OF WORK REVIEWED

70-XX Mechanics of particles and systems 70-08 Computational methods Banks, H. T. (Editor) 3 Control and estimation in distributed parameter systems 430 70Q05 Control of mechanical systems Banks, H. T. (Editor) 3 Control and estimation in distributed parameter systems 430 73-XX Mechanics of solids 73-06 Proceedings, conferences, collections, etc. Ciarlet, Philippe G., 40 Asymptotic methods for elastic struc- Trabucho, Lu´ıs, & tures 1760 Viano,˜ Juan M. (Editors)

73Cxx Elasticity Brenner, Susanne C., & 14 The mathematical theory of finite element Scott, L. Ridgway methods 877 73C50 Nonlinear elasticity Ciarlet, P. G., & Lions, J. L. 1 Handbook of numerical analysis 429 (Editors)

73K05 Beams, columns, rods Ciarlet, Philippe G., 40 Asymptotic methods for elastic struc- Trabucho, Lu´ıs, & tures 1760 Viano,˜ Juan M. (Editors)

73K10 Plates, discs, membranes Ciarlet, Philippe G., 40 Asymptotic methods for elastic struc- Trabucho, Lu´ıs, & tures 1760 Viano,˜ Juan M. (Editors)

73K15 Shells Ciarlet, Philippe G., 40 Asymptotic methods for elastic struc- Trabucho, Lu´ıs, & tures 1760 Viano,˜ Juan M. (Editors)

73U05 Thermomechanics of solids Vasil′eva, Adelaida B., 30 The boundary function method for singular Butuzov, Valentin F., & perturbation problems 1366 Kalachev, Leonid V. 73V20 Other numerical methods Ciarlet, P. G., & Lions, J. L. 1 Handbook of numerical analysis 429 (Editors)

73V25 Variational methods Ciarlet, Philippe G., 40 Asymptotic methods for elastic struc- Trabucho, Lu´ıs, & tures 1760 Viano,˜ Juan M. (Editors) 76-XX Fluid mechanics 76-06 Proceedings, conferences, collections, etc. Cohen, Gary (Editor) 31 Mathematical and numerical aspects of wave propagation 1369 INDEX OF REVIEWS BY SUBJECT OF WORK REVIEWED

76W05 Magnetohydrodynamics and electrohydrodynamics Brown, J. David, 6 Proceedings of the Cornelius Lanczos Chu, Moody T., international centenary conference 432 Ellison, Donald C., & Plemmons, Robert J. (Editors) 78-XX Optics, electromagnetic theory 78-06 Proceedings, conferences, collections, etc. Cohen, Gary (Editor) 31 Mathematical and numerical aspects of wave propagation 1369 78A30 Electro- and magnetostatics Vasil′eva, Adelaida B., 30 The boundary function method for singular Butuzov, Valentin F., & perturbation problems 1366 Kalachev, Leonid V. 80-XX Classical thermodynamics, heat transfer 80A25 Combustion, interior ballistics Vasil′eva, Adelaida B., 30 The boundary function method for singular Butuzov, Valentin F., & perturbation problems 1366 Kalachev, Leonid V. 82-XX Statistical mechanics, structure of matter 82Dxx Applications to specific types of physical systems 82D99 None of the above, but in this section Molenaar, J. 39 Multigrid methods for semiconductor device simulation 1758 83-XX Relativity and gravitational theory 83-06 Proceedings, conferences, collections, etc. Brown, J. David, 6 Proceedings of the Cornelius Lanczos Chu, Moody T., international centenary conference 432 Ellison, Donald C., & Plemmons, Robert J. (Editors) 83C05 Einstein’s equations Brown, J. David, 6 Proceedings of the Cornelius Lanczos Chu, Moody T., international centenary conference 432 Ellison, Donald C., & Plemmons, Robert J. (Editors) 85-XX Astronomy and astrophysics 85-06 Proceedings, conferences, collections, etc. Brown, J. David, 6 Proceedings of the Cornelius Lanczos Chu, Moody T., international centenary conference 432 Ellison, Donald C., & Plemmons, Robert J. (Editors) 86-XX Geophysics 86-06 Proceedings, conferences, collections, etc. Foufoula-Georgiou, Efi, & 9 Wavelets in geophysics 436 Kumar, Praveen (Editors) INDEX OF ERRATA

86-08 Computational methods Foufoula-Georgiou, Efi, & 9 Wavelets in geophysics 436 Kumar, Praveen (Editors)

92-XX Biology and other natural sciences, behavioral sciences 92C20 Neural biology Vasil′eva, Adelaida B., 30 The boundary function method for singular Butuzov, Valentin F., & perturbation problems 1366 Kalachev, Leonid V. 94-XX Information and communication, circuits 94-01 Instructional exposition Cox, Earl 4 The fuzzy systems handbook: A practi- tioner’s guide to building, using, and maintaining fuzzy systems 431

94A12 Signal theory Briggs, William L., & 33 The DFT: An owner’s manual for the Henson, Van Emden discrete Fourier transform 1371

94A60 Cryptography Lidl, Rudolf, & 36 Introduction to finite fields and their Niederreiter, Harald applications 1376

94B05 Linear codes, general Krishna, Hari, Krishna, Bal, 27 Computational number theory and digital Lin, Kuo-Yu, & signal processing: Fast algorithms and Sun, Jenn-Dong error control techniques 893

94B60 Other types of codes Lidl, Rudolf, & 36 Introduction to finite fields and their Niederreiter, Harald applications 1376

94D05 Fuzzy sets and logic Cox, Earl 4 The fuzzy systems handbook: A practi- tioner’s guide to building, using, and maintaining fuzzy systems 431

INDEX OF ERRATA

No. Author Title Page

626 Apelblat, A. Table of definite and infinite integrals ...... 1386 622 Erdelyi,´ A. (Editor), Tables of integral transforms, Vol. I ...... 1384 Magnus, W., Oberhettinger, F., & Tricomi, F. G. (research associates) 623 Erdelyi,´ A. (Editor), Tables of integral transforms, Vol. II ...... 1385 Magnus, W., Oberhettinger, F., & Tricomi, F. G. (research associates) INDEX OF ERRATA

624 Erdelyi,´ A. (Editor), Higher transcendental functions, Vol. I ...... 1385 Magnus, W., Oberhettinger, F., & Tricomi, F. G. (research associates) 627 Gradshteyn, I. S., & Table of integrals, series, and products ...... 1769 Ryzhik, I. M. 625 Oberhettinger, F. Tables of Bessel transforms ...... 1386 619 Prudnikov, A. P, Integrals and series, Vol. 1, Elementary func- Brychkov, Yu. A., & tions ...... 1380 Marichev, O. I 620 Prudnikov, A. P., Integrals and series, Vol. 2, Special functions 1382 Brychkov, Yu. A., & Marichev, O. I. 621 Prudnikov, A. P., Integrals and series, Vol. 3, More special func- Brychkov, Yu. A., & tions ...... 1384 Marichev, O. I. 618 Weber, Heinrich Lehrbuch der Algebra, Vol. 3 ...... 1379

INDEX OF CORRIGENDA Beyer, W. A. and Roof, The lattice structure of multiplicative congruential R. B. and Williamson, pseudo-random vectors ...... 445 Dorothy

INDEX OF SUPPLEMENTS Boyd, David W. Supplement to “On the beta expansion for Salem numbers of degree 6” ...... Apr. Langtry, T. N. An application of Diophantine approximation to the construction of rank-1 lattice quadrature rules (microfiche supplement) ...... Oct. Lukes, R. F., Patterson, Supplement to “Some results on pseudosquares” . . . . . Jan. C. D., & Williams, H. C. Urabe, Tohsuke Supplement to “Calculation of Manin’s invariant for Del Pezzo surfaces” ...... Jan. Yang, Huanan Supplement to “On wavewise entropy inequalities for high resolution schemes I: The semidiscrete case” ...... Jan. M THE ATI A CA M L ΤΡΗΤΟΣ ΜΗ

N ΕΙΣΙΤΩ S A O

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ΑΓΕΩΜΕ

VOLUME 65 Y 1996

M A

F O 8 U 88 NDED 1 MATHEMATICS OF COMPUTATION

A M E R I C A N M A T H E M A T I C A L S O C I E T Y

EDITED BY James H. Bramble Susanne C. Brenner Howard Elman Richard S. Falk Walter Gautschi Daniel W. Lozier James N. Lyness Harald Niederreiter Syvert P. Nørsett Andrew M. Odlyzko John E. Osborn Stanley Osher Carl Pomerance René Schoof L. Ridgway Scott Daniel Shanks Chi-Wang Shu Frank Stenger Hans J. Stetter G. W. Stewart Nico M. Temme Vidar Thomée Lars B. Wahlbin, Managing Editor Joseph D. Ward Hugh C. Williams John W. Wrench, Jr. Stephen J. Wright

PROVIDENCE, RHODE ISLAND USA ISSN 0025-5718 Mathematics of Computation This journal publishes research articles in computational mathematics. Areas covered include numerical analysis, with emphasis on the mathematical analysis and development of methods, computational number theory and algebra, and related fields. Table errata and reviews of books in areas related to computational mathematics are also included. Submission information. See Information for Authors at the end of this issue. Subscription information. Mathematics of Computation is published quarterly. Be- ginning in January 1996 Mathematics of Computation is accessible from e-MATH via the World Wide Web at the URL http : //www.ams.org/publications/. Subscription prices for Volume 65 (1996) are as follows: for paper delivery, $290 list, $232 institutional mem- ber, $261 corporate member, $189 MAA & SIAM members; $174 individual member; for electronic delivery, $261 list, $209 institutional member, $235 corporate member, $170 MAA & SIAM members, $157 individual member; for combination paper and electronic delivery, $334 list, $267 insititutional member, $301 corporate member, $217 MAA & SIAM members, $200 individual member. If ordering the paper version, add $9 for sur- face delivery outside the United States and India; $18 to India. Expedited delivery to destinations in North America is $13; elsewhere $40. Back number information. For back issues see the AMS Catalog of Publications. Subscriptions and orders should be addressed to the American Mathematical Society, P.O. Box 5904, Boston, MA 02206-5904. All orders must be accompanied by payment. Other correspondence should be addressed to P.O. Box 6248, Providence, RI 02940-6248. Unpublished Mathematical Tables. The editorial office of the journal maintains a repository of Unpublished Mathematical Tables (UMT). When a table is deposited in the UMT repository a brief summary of its contents is published in the section Reviews and Descriptions of Tables and Books. Upon request, the chairman of the editorial committee will supply copies of any table for a nominal cost per page. All tables and correspondence concerning the UMT should be sent to Lars B. Wahlbin, Chairman, Editorial Committee, Mathematics of Computation, Center for Applied Mathematics, 657 Frank H. T. Rhodes Hall, Cornell University, Ithaca, NY 14853. Copying and reprinting. Material in this journal may be reproduced by any means for educational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents and provided that the customary acknowledgment of the source is given. This consent does not extend to other kinds of copying for general distribution, for advertising or promotional purposes, or for resale. Requests for permission for commercial use of material should be addressed to the Assistant to the Publisher, American Mathematical Society, P.O. Box 6248, Providence, RI 02940-6248. Requests can also be made by e-mail to [email protected]. Excluded from these provisions is material in articles for which the author holds copy- right. In such cases, requests for permission to use or reprint should be addressed directly to the author(s). (Copyright ownership is indicated in the notice in the lower right-hand corner of the first page of each article.)

Mathematics of Computation is published quarterly by the American Mathematical Society at 201 Charles Street, Providence, RI 02904-2213. Periodicals postage is paid at Providence, Rhode Island. Postmaster: Send address changes to Mathematics of Compu- tation, American Mathematical Society, P. O. Box 6248, Providence, RI 02940-6248.

c 1996 by the American Mathematical Society. All rights reserved. This journal is indexed in Science Citation Index r, SciSearchr, Research Alert r, CompuMath Citation Index r, and Current Contentsr/Physical, Chemical & Earth Sciences. ∞ The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. 10987654321 010099989796 MATHEMATICS OF COMPUTATION CONTENTS Vol. 65, No. 213 January 1996

Ch. Lubich, I. H. Sloan, and V. Thom´ee, Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term ...... 1 Alfred H. Schatz and Junping Wang, Some new error estimates for Ritz– Galerkin methods with minimal regularity assumptions ...... 19 R. A. Nicolaides and X. Wu, Analysis and convergence of the MAC scheme. II. Navier-Stokes equations ...... 29 Huanan Yang, On wavewise entropy inequalities for high-resolution schemes. I: The semidiscrete case ...... 45 Carsten Carstensen, Efficiency of a posteriori BEM–error estimates for first-kind integral equations on quasi–uniform meshes ...... 69 Charles K. Chui and Dong Hong, Construction of local C1 quartic spline elements for optimal-order approximation ...... 85 Charles K. Chui and Johan M. De Villiers, Applications of optimally local interpolation to interpolatory approximants and compactly supported wavelets ...... 99 Urs von Matt and G. W. Stewart, Rounding errors in solving block Hessenberg systems ...... 115 V. V. Strela and E. E. Tyrtyshnikov, Which circulant preconditioner is better? ...... 137 Arno B. J. Kuijlaars, The zeros of Faber polynomials generated by an m- star ...... 151 David M. Smith, A multiple -precision division algorithm ...... 157 J. N. Lyness and S. Joe, Triangular canonical forms for lattice rules of prime-power order ...... 165 Christian L´ecot, Error bounds for quasi-Monte Carlo integration with nets 179 Raymond Couture and Pierre L’Ecuyer, Orbits and lattices for linear random number generators with composite moduli ...... 189 Pierre L’Ecuyer, Maximally equidistributed combined Tausworthe genera- tors ...... 203 J¨urgen Eichenauer-Herrmann and Frank Emmerich, Compound inversive congruential pseudorandom numbers: an average-case analysis 215 Takashi Kato, Li-Ming Wu, and Niro Yanagihara, On a nonlinear congruential pseudorandom number generator ...... 227 M. Deleglise and J. Rivat, Computing π(x): the Meissel, Lehmer, Lagarias, Miller, Odlyzko method ...... 235 Tohsuke Urabe, Calculation of Manin’s invariant for Del Pezzo surfaces . 247 Gregory S. Call and Joseph H. Silverman, Computing the canonical height on K3 surfaces ...... 259 Kimberly Pearson, Integral cohomology and detection of w-basic 2-groups 291 V. Flammang, Two new points in the spectrum of the absolute Mahler measure of totally positive algebraic integers ...... 307 T. Fukuda and K. Komatsu, A capitulation problem and Greenberg’s conjecture on real quadratic fields ...... 313 M. Daberkow and M. Pohst, On integral bases in relative quadratic extensions ...... 319 Wen Bao Han, The coefficients of primitive polynomials over finite fields . 331 Maurice Mignotte, Attila Peth¨o,and Ralf Roth, Complete solutions of a family of quartic Thue and index form equations ...... 341 W. S. Anglin, Simultaneous Pell equations ...... 355 R. F. Lukes, C. D. Patterson, and H. C. Williams, Some results on pseudosquares ...... 361 Ronald Joseph Burthe, Jr., Further investigations with the strong probable prime test ...... 373 Samuel S. Wagstaff, Jr., Aurifeuillian factorizations and the period of the Bell numbers modulo a prime ...... 383 Harvey Dubner, Large Sophie Germain primes ...... 393 Olivier Ramar´eand Robert Rumely, Primes in arithmetic progressions 397 Karl-Heinz Indlekofer and Antal J´arai, Largest known twin primes . . 427 Reviews and Descriptions of Tables and Books ...... 429 Ciarlet and Lions, Editors 1, Lions and Baiocchi, Editors 2, Banks, Editor 3, Cox 4, Dikshit and Micchelli, Editors 5, Brown, Chu, Ellison, and Plemmons, Editors 6, Laurent, le M´ehaut´e,and Schumaker, Editors 7, Wickenhauser 8, Foufoula-Georgiou and Kumar, Editors 9, Milovanovi´c,Mitrinovi´c,and Rassias 10, Rubio 11, Bailey, Bjørstad, Gilbert, Mascagni, Schreiber, Simon, Torczon, and Watson, Editors 12, Cohen 13 Corrigendum ...... 445 Supplement to “On wavewise entropy inequalities for high-resolution schemes. I: The semidiscrete case” by Huanan Yang ...... S1 Supplement to “Calculation of Manin’s invariant for Del Pezzo surfaces” by Tohsuke Urabe ...... S15 Supplement to “Some results on pseudosquares” by R. F. Lukes, C. D. Patterson, and H. C. Williams ...... S25

Vol. 65, No. 214 April 1996

Torgeir Rusten, Panayot S. Vassilevski, and Ragnar Winther, Interior penalty preconditioners for mixed finite element approximations of elliptic problems ...... 447 Zhangxin Chen, Richard E. Ewing, and Raytcho Lazarov, Domain decomposition algorithms for mixed methods for second-order elliptic problems ...... 467 Donald A. French and Todd E. Peterson, A continuous space-time finite element method for the wave equation ...... 491 Laurence Halpern, Spectral methods in polar coordinates for the Stokes problem. Application to computation in unbounded domains ...... 507 Bernardo Cockburn and Pierre-Alain Gremaud, A priori error estimates for numerical methods for scalar conservation laws. Part I: The general approach ...... 533 Haim Nessyahu, Convergence rate of approximate solutions to weakly coupled nonlinear systems ...... 575 Yuesheng Xu and Yunhe Zhao, An extrapolation method for a class of boundary integral equations ...... 587 Evangelos A. Coutsias, Thomas Hagstrom, and David Torres, An efficient spectral method for ordinary differential equations with rational function coefficients ...... 611 Rajendra Bhatia and Ren-Cang Li, On perturbations of matrix pencils with real spectra. II ...... 637 R. C. Gayle and J. M. Wolfe, Unicity in piecewise polynomial L1-approximation via an algorithm ...... 647 Peter Borwein and Tam´asErd´elyi, The integer Chebyshev problem . . . 661 Ewald Quak, Trigonometric wavelets for Hermite interpolation ...... 683 W. Lawton, S. L. Lee, and Zuowei Shen, An algorithm for matrix extension and wavelet construction ...... 723 Dirk P. Laurie, Anti-Gaussian quadrature formulas ...... 739 Frank Emmerich, Pseudorandom vector generation by the compound inversive method ...... 749 Takashi Kato, Li-Ming Wu, and Niro Yanagihara, The serial test for a nonlinear pseudorandom number generator ...... 761 Charles H. Jepsen, Dissections of p : q rectangles ...... 771

Hisao Taya, Computation of Z3-invariantsof real quadratic fields ...... 779 Christian Wagner, Class number 5, 6 and 7 ...... 785 Istv´anGa´al, Computing all power integral bases in orders of totally real cyclic sextic number fields ...... 801 G¨unter L¨ohand Wolfgang Niebuhr, A new algorithm for constructing large Carmichael numbers ...... 823 P. Erd˝osand Mordechai Lewin, d-complete sequences of integers ...... 837 David W. Boyd, On beta expansions for Pisot numbers ...... 841 David W. Boyd, On the beta expansion for Salem numbers of degree 6 . . 861 Reviews and Descriptions of Tables and Books ...... 877 Brenner and Scott 14, Friedman and Littman 15, Dongarra and Tourancheau, Editors 16, Gander and Hˇreb´ıˇcek 17, Abell and Braselton 18, Mangasarian 19, Nesterov and Nemirovskii 20, Axelsson 21, Bini and Pan 22, Micchelli 23, Chui, Montefusco and Puccio, Editors 24, Farin 25, Sapidis, Editor 26, Krishna, Krishna, Lin and Sun 27, Sloane and Ploufee 28 Supplement to “On the beta expansion for Salem numbers of degree 6” by David W. Boyd ...... S29 Vol. 65, No. 215 July 1996

Susanne C. Brenner, Two-level additive Schwarz preconditioners for nonconforming finite element methods ...... 897 Peter Oswald, Preconditioners for nonconforming discretizations ...... 923 Yuanhua Deng, Goong Chen, Wei-Ming Ni, and Jianxin Zhou, Boundary element monotone iteration scheme for semilinear elliptic partial differential equations ...... 943 Rob Stevenson, The frequency decomposition multilevel method: A robust additive hierarchical basis preconditioner ...... 983 M. Vanmaele and R. Van Keer, On a variational approximation method for a class of elliptic eigenvalue problems in composite structures . . . . . 999 MalgorzataPeszy´nska, Finite element approximation of diffusion equations with convolution terms ...... 1019 Jie Shen, On error estimates of the projection methods for the Navier-Stokes equations: Second-order schemes ...... 1039 Johan F. Malmliden and N. Anders Petersson, A fast iterative method to compute the flow around a submerged body ...... 1067 Guangfu Sun and Martin Stynes, A uniformly convergent method for a singularly perturbed semilinear reaction–diffusion problem with multiple solutions ...... 1085 Petr Klouˇcek, Bo Li and Mitchell Luskin, Analysis of a class of nonconforming finite elements for crystalline microstructures ...... 1111 Hailiang Liu and Jinghua Wang, Nonlinear stability of stationary discrete shocks for nonconvex scalar conservation laws ...... 1137 Sebastian Noelle, A note on entropy inequalities and error estimates for higher-order accurate finite volume schemes on irregular families of grids 1155 S. N. Papakostas and G. Papageorgiou, A family of fifth-order Runge- Kutta pairs ...... 1165 Anwei Liu and Barry Joe, Quality local refinement of tetrahedral meshes based on 8-subtetrahedron subdivision ...... 1183 Annamaria Palamara Orsi, Product integration for Volterra integral equations of the second kind with weakly singular kernels ...... 1201 Ronald B. Morgan, On restarting the Arnoldi method for large non-symmetric eigenvalue problems ...... 1213 Carl de Boor, On the Sauer-Xu formula for the error in multivariate polynomial interpolation ...... 1231 V. Demichelis, Quasi-interpolatory splines based on Schoenberg points . . . 1235 Walter Gautschi and Shikang Li, On quadrature convergence of extended Lagrange interpolation ...... 1249 Walter Gautschi and Sotirios E. Notaris, Stieltjes polynomials and related quadrature formulae for a class of weight functions ...... 1257 Dimitar K. Dimitrov, Integration of polyharmonic functions ...... 1269 B.G.S. Doman, An asymptotic expansion for the incomplete beta function 1283 A. J. W. Duijvestijn, The number of polyhedral (3-connected planar) graphs ...... 1289 Harvey Cohn and John McKay, Spontaneous generation of modular invariants ...... 1295 Johannes Buchmann and Victor Shoup, Constructing nonresidues in finite fields and the extended Riemann hypothesis ...... 1311 Wieb Bosma and Peter Stevenhagen, Density computations for real quadratic units ...... 1327 Takashi Fukuda, Cyclotomic units and Greenberg’s conjecture for real quadratic fields ...... 1339 A. Y. Cheer and D. A. Goldston, Tur´an’spure power sum problem . . . 1349 A.J.W. Duijvestijn, Simple perfect squared squares and 2 × 1 squared rectangles of order 26 ...... 1359 Reviews and Descriptions of Tables and Books ...... 1365 Kˇr´ıˇzek,Neittaanm¨aki,and Stenberg, Editors 29, Vasil′eva, Butuzov, and Kalachev 30, Cohen, Editor 31, Coombes, Hunt, Lipsman, Osborn, and Stuck 32, Briggs and Henson 33, Lau 34, Zahar, Editor 35, Lidl and Niederreiter 36, Riesel 37 Table Errata ...... 1379

Vol. 65, No. 216 October 1996

Jan Mandel and Marian Brezina, Balancing domain decomposition for problems with large jumps in coefficients ...... 1387 Christoph Schwab and Manil Suri, The p and hp versions of the finite element method for problems with boundary layers ...... 1403 Zhimin Zhang, Ultraconvergence of the patch recovery technique ...... 1431 F. Bouchut, Ch. Bourdarias, and B. Perthame, A MUSCL method satisfying all the numerical entropy inequalities ...... 1439 Rodolfo Rodr´ıguez and Jorge E. Solomin, The order of convergence of eigenfrequencies in finite element approximations of fluid-structure interaction problems ...... 1463 T. Y. Li and Xiaoshen Wang, The BKK root count in Cn ...... 1477 Mar´ıa-Cecilia Rivara and Gabriel Iribarren, The 4-triangles longest-side partition of triangles and linear refinement algorithms ...... 1485 S. M. Rump, Expansion and estimation of the range of nonlinear functions 1503 Amos Ron and Xingping Sun, Strictly positive definite functions on spheresin Euclidean spaces ...... 1513 Iaci Malta, Nicolau C. Saldanha, and Carlos Tomei, The numerical inversion of functions from the plane to the plane ...... 1531 R. T. Farouki and T. N. T. Goodman, On the optimal stability of the Bernstein basis ...... 1553 Laura Gori and Charles A. Micchelli, On weight functions which admit explicit Gauss-Tur´anquadrature formulas ...... 1567 Ronald Cools and Ian H. Sloan, Minimal cubature formulae of trigonometric degree ...... 1583 Yu-lin Xu, Fast evaluation of the Gaunt coefficients ...... 1601 J. B. Keiper, On the zeros of the Ramanujan τ-Dirichlet series in the critical strip ...... 1613 S. Heinrich, Efficient algorithms for computing the L2-discrepancy ...... 1621 T. N. Langtry, An application of Diophantine approximation to the construction of rank-1 lattice quadrature rules ...... 1635 Vincenzo Acciaro, Solvability of norm equations over cyclic number fields of prime degree ...... 1663 David A. Clark, Non-Galois cubic fields which are Euclidean but not norm- Euclidean ...... 1675 Henri Cohen, Hermite and Smith normal form algorithms over Dedekind domains ...... 1681 Eric Bach and Ren´ePeralta, Asymptotic semismoothness probabilities 1701 Eric Bach and Jonathan Sorenson, Explicit bounds for primes in residue classes ...... 1717 Eric Bach, Richard Lukes, Jeffrey Shallit, and H. C. Williams, Results and estimates on pseudopowers ...... 1737 Brienne E. Brown and Daniel M. Gordon, On sequences without geometric progressions ...... 1749 Randy L. Ekl, Equal sums of four seventh powers ...... 1755 Reviews and Descriptions of Tables and Books ...... 1757 Deuflhard and Hohmann 38, Molenaar 39, Ciarlet, Trabucho, and Via˜no,Editors 40, Shikin and Plis 41, Sobol’ 42, Fiume 43, Sabot, Editor 44, Anderson, Bai, Bischof, Demmel, Dongarra, du Croz, Greenbaum, Jammarling, McKenney, Ostrouchov, and Sorensen 45, Abell and Braselton 46, Stepanov 47 Table Errata ...... 1769 Microfiche Supplement Editorial Information As of June 30, 1996, the backlog for this journal was approximately 0 issues. This esti- mate is the result of dividing the number of manuscripts for this journal in the Providence office that have not yet gone to the printer on the above date by the average number of articles per issue over the previous twelve months, reduced by the number of issues published in six months (the time necessary for editing and composing a typical issue). A Consent to Publish and Copyright Agreement is required before a paper will be published in this journal. By submitting a paper to this journal, authors certify that the results have not been submitted to nor are they under consideration for publication by another journal, conference proceedings, or similar publication.

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Editorial Committee ANDREW M. ODLYZKO, AT&T Bell Laboratories, 600 Mountain Avenue, Murray Hill, NJ 07974; E-mail: [email protected] STANLEY OSHER, Department of Mathematics, University of California, Los Angeles, CA 90024; E-mail: [email protected] G. W. STEWART, Department of Computer Science, University of Maryland, College Park, MD 20742; E-mail: [email protected] LARS B. WAHLBIN, Chairman. Center for Applied Mathematics, 657 Frank H. T. Rhodes Hall, Cornell University, Ithaca, NY 14853-3801; E-mail: [email protected]. edu Board of Associate Editors JAMES H. BRAMBLE, Department of Mathematics, Texas A & M University, College Station, TX 77843-3368; E-mail: [email protected] SUSANNE C. BRENNER, Department of Mathematics, University of South Carolina, Columbia, SC 29208; E-mail: [email protected] HOWARD ELMAN, Department of Computer Science, University of Maryland, College Park, MD 20742; E-mail: [email protected] RICHARD S. FALK, Department of Mathematics, Rutgers University, New Brunswick, NJ 08903-2101; E-mail: [email protected] WALTER GAUTSCHI, Department of Computer Sciences, Purdue University, West Lafayette, IN 47907; E-mail: [email protected] DANIEL W. LOZIER, Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899-0001; E-mail: dlozier@ nist.gov JAMES N. LYNESS, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439; E-mail: [email protected] HARALD NIEDERREITER, Institute for Information Processing, Austrian Academy of Sciences, Sonnenfelsgasse 19, A-1010 Vienna, Austria; E-mail: [email protected]. ac.at SYVERT P. NØRSETT, Division of Numerical Mathematics, The University of Trond- heim and The Norwegian Institute of Technology, Alfred Getz vei 1, N-7034 Trondheim- NTH, Norway; E-mail: [email protected] JOHN E. OSBORN, Department of Mathematics, University of Maryland, College Park, MD 20742; E-mail: [email protected] CARL POMERANCE, Department of Mathematics, The University of Georgia, Athens, GA 30602; E-mail: [email protected] RENE´ SCHOOF, Dipartimento di Matematica, 2a Universit`adi Roma “Tor Vergata”, I-00133 Roma, Italy; E-mail: [email protected]; and schoof@fwi. uva.nl L. RIDGWAY SCOTT, Department of Mathematics, University of Houston, Houston, TX 77204-3476; E-mail: [email protected] DANIEL SHANKS, Department of Mathematics, University of Maryland, College Park, MD 20742; E-mail: [email protected] CHI-WANG SHU, Applied Mathematics Division, Brown University, Providence, RI 02912-0001; E-mail: [email protected] FRANK STENGER, Department of Computer Science, University of Utah, Salt Lake City, UT 84112; E-mail: [email protected] HANS J. STETTER, Institut f¨ur Numerische Mathematik, Technische Universit¨at Wien, Wiedner Hauptstrasse 6-10, A-1040, Wien, Austria; E-mail: stetter@uranus. tuwien.ac.at NICO M. TEMME, Stichting Mathematisch Centrum, Centrum voor Wiskunde en Informatica, Kruislaan 413, 1098 SJ Amsterdam, The Netherlands; E-mail: [email protected] VIDAR THOMEE,´ Mathematics Department, Chalmers University of Technology, S- 412 96 G¨oteborg, Sweden; E-mail: [email protected] JOSEPH D. WARD, Department of Mathematics, Texas A & M University, College Station, TX 77843-3368; E-mail: [email protected] HUGH C. WILLIAMS, Department of Computer Science, University of Manitoba, Win- nipeg, Manitoba, Canada R3T 2N2; E-mail: Hugh [email protected] JOHN W. WRENCH, JR., 102 Mt. Olivet Boulevard, Frederick, MD 21701 STEPHEN J. WRIGHT, Mathematics and Computer Science Division, Argonne Na- tional Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439; E-mail: [email protected] (Continued from back cover) Eric Bach and Jonathan Sorenson, Explicit bounds for primes in residue classes ...... 1717 Eric Bach, Richard Lukes, Jeffrey Shallit, and H. C. Williams, Results and estimates on pseudopowers ...... 1737 Brienne E. Brown and Daniel M. Gordon, On sequences without geometric progressions ...... 1749 Randy L. Ekl, Equal sums of four seventh powers ...... 1755 Reviews and Descriptions of Tables and Books ...... 1757 Deuflhard and Hohmann 38, Molenaar 39, Ciarlet, Trabucho, and Via˜no,Editors 40, Shikin and Plis 41, Sobol’ 42, Fiume 43, Sabot, Editor 44, Anderson, Bai, Bischof, Demmel, Dongarra, du Croz, Greenbaum, Jammarling, McKenney, Ostrouchov, and Sorensen 45, Abell and Braselton 46, Stepanov 47 Table Errata ...... 1769 Microfiche Supplement