Bibliography [A63] S. J. Aarseth, Dynamical Evaluation of Clusters of Galaxies-I, Monthly Notices of the Royal Astronomical Society, 126,223-255,1963. [A78] K. E. Atkinson, An Introduction to Numerical Analysis, Wiley, New York, 1978. [A85] A. W. Appel, An Efficient Program for Many-Body Simulation, SIAM Journal on Scientific and Statistical Computing, 6,85-103, 1985. [A86] C. R. Anderson, A Method of Local Corrections for Computing the Veloc­ ity Field due to a Distribution of Vortex Blobs, Journal of Computational Physics, 62,111-123,1986. [A89] J. Abbott, Recovery of Algebraic Numbers from their p-adic Approxima­ tions, Proceedings of International Symposium on Symbolic and Algebraic Computation (ISSAC'89), 112-120, ACM Press, New York, 1989. [AB91] I. Adler, P. Beiling, Polynomial Algorithms for LP over a Subring of the Algebraic Integers with Applications to LP with Circulant Matrices, Pro­ ceedings of 32nd Annual IEEE Symposium on Foundations of Computer Science (FOCS'9I), 480-487, IEEE Computer Society Press, Washington, DC, 1991. [ABM99] 1. Abbott, M. Bronstein, T. Mulders, Fast Deterministic Computations of the Determinants of Dense Matrices, Proceedings of International Sympo­ sium on Symbolic and Algebraic Computation (ISSAC'99), 197-204, ACM Press, New York, 1999. [ABKW90] A. C. Antoulas, 1. A. Ball, J. Kang, J. C. Willems, On the Solution of the Minimal Rational Interpolation Problem, Linear Algebra and Its Applica­ tions, 137-138,479-509, 1990. [AG89] G. S. Ammar, P. Gader, New Decompositions of the Inverse of a Toeplitz Matrix, Proceedings of 1989 International Symposium on Mathematical Theory of Networks and Systems (MTNS'89), III, 421-428, Birkhauser, Boston, 1989. V. Y. Pan, Structured Matrices and Polynomials © Birkhäuser Boston 2001 244 Bibliography [AG91] G. S. Ammar, P. Gader, A Variant of the Gohberg-Semencul Formula In­ volving Circulant Matrices, SIAM Journal on Matrix Analysis and Appli­ cations, 12,3,534-541,1991. [AGr88] G. S. Ammar, W. G. Gragg, Superfast Solution of Real Positive Definite Toeplitz Systems, SIAM Journal on Matrix Analysis and Applications, 9, 1,61-76, 1988. [AHU74] A. V. Abo, J. E. Hopcroft, J. D. Ullman, The Design and Analysis of Com­ puter Algorithms, Addison-Wesley, Reading, Massachusetts, 1974. [ANR74] N. Ahmed, T. Natarajan, K. Rao, Discrete Cosine Transforms, IEEE Trans­ action on Computing, 23, 90--93, 1974. [AI85] H. Alt, Multiplication Is the Easiest Nontrivial Arithmetic Function, Theo­ retical Computer Science, 36, 333-339, 1985. [ASU75] A. v. Aho, V. Steiglitz, J. D. Ullman, Evaluation of Polynomials at Fixed Sets of Points, SIAM Journal on Computing, 4, 533-539,1975. [B40] E. T. Bell, The Development of Mathematics, McGraw-Hill, New York, 1940. [B68] E. H. Bareiss, Sylvester's Identity and Multistep Integer-Preserving Gaus­ sian Elimination, Mathematics of Computation, 22, 565-578, 1968. [B76] R. P. Brent, Fast Multiple-Precision Evaluation of Elementary Functions, Journal ofACM, 23, 242-251, 1976. [B81] S. Barnett, Generalized Polynomials and Linear Systems Theory, Proceed­ ings of3rd IMA Conference on Control Theory, 3-30, 1981. [B83] D. A. Bini, On a Class of Matrices Related to Toeplitz Matrices, TR-83-5, Computer Science Department, SUNYA, Albany, New York, 1983. [B84] D. A. Bini, Parallel Solution of Certain Toeplitz Linear Systems, SIAM Journal on Computing, 13, 2, 268-279,1984. [B85] J. R. Bunch, Stability of Methods for Solving Toeplitz Systems of Equa­ tions, SIAM Journal on Scientific and Statistical Computing, 6, 2,349-364, 1985. [B88] J. Barnes, Encounters of DisklHalo Galaxies, The Astrophisical Journal, 331,699, 1988. [Ba] D. J. Bernstein, Multidigit Multiplication for Mathematicians, Advances in Applied Mathematics, to appear. [BA80] R. R. Bitrnead, B. D. O. Anderson, Asymptotically Fast Solution of Toeplitz and Related Systems of Linear Equations, Linear Algebra and Its Applications, 34,103-116,1980. Bibliography 245 [BB84] J. W. Borwein, P. B. Borwein, The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions, SIAM Review, 26, 3, 351-366, 1984. [BC83] D. A. Bini, M. Capovani, Spectral and Computational Properties of Band Symmetric Toeplitz Matrices, Linear Algebra and Its Applications, 52/53, 99-126,1983. [Be68] E. R. Berlekamp, Algebraic Coding Theory, McGraw-Hill, New York, 1968. [BDB90] D. A. Bini, F. Di Benedetto, A New Preconditioner for the Parallel Solu­ tion of Positive Definite Toeplitz Systems, Proceedings of 2nd ACM Sym­ posium on Parallel Algorithms and Architectures, 220--223, ACM Press, New York, 1990. [BE73] A. Bjorck, T. Elfving, Algorithms for Confluent Vandermonde Systems, Numerische Mathematik, 21,130--137,1973. [BEPP99] H. Bronnimann, I. Z. Emiris, S. Pion, V. Y. Pan, Sign Determination in Residue Number Systems, Theoretical Computer Science, 210, 1, 173- 197,1999. [BF93] D. A. Bini, P. Favati, On a Matrix Algebra Related to the Discrete Hartley Transform, SIAM Journal on Matrix Analysis and Applications, 14, 500- 507,1993. [BG95] D. A. Bini, L. Gemignani, Fast Parallel Computation of the Polynomial Remainder Sequence via Bezout and Hankel Matrices, SIAM Journal on Computing, 24, 63-77, 1995. [BGH82] A. Borodin, J. von zur Gathen, J. Hopcroft, Fast Parallel Matrix and GCD Computation, Information and Control, 52,3,241-256,1982. [BG-M96] G. A. Backer Jr., P. Graves-Morris, Pade Approximants, in Encyclopedia of Mathematics and Its Applications, 59, Cambridge University Press, Com­ bridge, UK, 1996 (2nd edition; 1st edition by Addison-Wesley, Reading, Massachusetts, 1982,2 volumes). [BGR90] J. A. Ball, I. Gohberg, L. Rodman, Interpolation of Rational Matrix Func­ tions, Operator Theory: Advances and Applications, 45, Birkhauser, Basel, 1990. [BGR90a] J. A. Ball, I. Gohberg, L. Rodman, Nehari Interpolation Problem for Ra­ tional Matrix Functions: the Generic Case, Roo-control Theory (E. Mosca and L. Pandolfi, editors), 277-308, Springer, Berlin, 1990. [BGY80] R. P. Brent, F. G. Gustavson, D. Y. Y. Yun, Fast Solution of Toeplitz Sys­ tems of Equations and Computation of Pade Approximations, Journal of Algorithms, 1,259-295, 1980. 246 Bibliography [B-I66] A. Ben-Israel, A Note on Iterative Method for Generalized Inversion of Matrices, Mathematics of Computation, 20, 439-440,1966. [B-IC66] A. Ben-Israel, D. Cohen, On Iterative Computation of Generalized Inverses and Associated Projections, SIAM Journal on Numerical Analysis, 3, 410- 419,1966. [BK78] R. P. Brent, H. T. Kung, Fast Algorithms for Manipulating Formal Power Series, Journal ofACM, 25, 4, 581-595,1978. [BK87] A. Bruckstein, T. Kailath, An Inverse Scattering Framework for Several Problems in Signal Processing, IEEE A SSP Magazine, 6-20, January 1987. [BM71] A. Borodin, I. Munro, Evaluation of Polynomials at Many Points, Informa­ tion Processing Letters, 1,2,66-68, 1971. [BM74] A. Borodin, R. Moenck, Fast Modular Transforms, Journal of Computer and Systems Sciences, 8,3,366-386, 1974. [BM75] A. Borodin, I. Munro, The Computational Complexity of Algebraic and Numeric Problems, American Elsevier, New York, 1975. [BM99] D. A. Bini, B. Meini, Fast Algorithms with Applications to Markov Chains and Queuing Models, Fast Reliable Algorithms for Matrices with Struc­ tures (T. Kailath and A. H. Sayed, editors), 211-243, SIAM Publications, Philadelphia, 1999. [BM01] D. A. Bini, B. Meini, Solving Block Banded Block Toeplitz Systems with Structured Blocks: Algorithms and Applications, in Structured Matrices: Recent Developments in Theory and Computation (D. A. Bini, E. Tyrtysh­ nikov, and P. Yalamov, editors), Nova Science, 2001. [BMa] D. A. Bini, B. Meini, Approximate Displacement Rank and Applications, preprint. [B068] C. A. Boyer, A History of Mathematics, Wiley, New York, 1968. [B-083] M. Ben-Or, Lower Bounds for Algebraic Computation Trees, Proceedings of 15th Annual ACM Symposium on Theory of Computing (STOC' 83), 80- 86, ACM Press, New York, 1983. [B-0T88] M. Ben-Or, P. Tiwari, A Deterministic Algorithm for Sparse Multivariate Polynomial Interpolation, Proceedings of20th Annual ACM Symposium on Theory of Computing (STOC'88), 301-309, ACM Press, New York, 1988. [BP70] A. Bj6rck, V. Pereyra, Solution of Vandermonde Systems of Equations, Mathematics of Computation, 24,893-903,1970. [BP86] D. A. Bini, V. Y. Pan, Polynomial Division and Its Computational Com­ plexity, J Complexity, 2, 179-203, 1986. Bibliography 247 [BP88] D. A. Bini, V. Y. Pan, Efficient Algorithms for the Evaluation of the Eigen­ values of (Block) Banded Toeplitz Matrices, Mathematics of Computation, 50,182,431-448,1988. [BP91] D. A. Bini, V. Y. Pan, Parallel Complexity of Tridiagonal Symmetric Eigen­ value Problem, Proceedings of2nd Annual ACM-SIAM Symposium on Dis­ crete Algorithms (SODA '91),384-393, ACM Press, New York, and SIAM Publications, Philadelphia, January 1991. [BP91a] D. A. Bini, V. Y. Pan, On the Evaluation of the Eigenvalues of a Banded Toeplitz Block Matrix, Journal of Complexity, 7, 408-424,1991. [BP92] D. A. Bini, V. Y. Pan, Practical Improvement of the Divide-and-Conquer Eigenvalue Algorithms, Computing, 48,109-123,1992. [BP93] D. A. Bini, V. Y. Pan, Improved Parallel Computations with Toeplitz-like and Hankel-like Matrices, Linear Algebra and Its Applications, 188/189, 3-29,1993. [BP94] D. A. Bini, V. Y. Pan, Polynomial and Matrix Computations, Vol.1: Fun­ damental Algorithms, Birkhauser, Boston, 1994. [BP96] D. A. Bini, V. Y. Pan, Graeffe's Chebyshev-like, and Cardinal's Processes for Spliting a Polynomial into Factors, Journal of Complexity, 12, 492- 511,1996. [BP98] D. A. Bini, V. Y. Pan, Computing Matrix Eigenvalues and Polynomial Ze­ ros Where the Output is Real, SIAM Journal on Computing, 27, 4, 1099- 1115, 1998. [BPa] D. A. Bini, V. Y. Pan, Polynomial and Matrix Computations, Vol.2: Fun­ damental and Practical Algorithms, Birkhauser, Boston, to appear. [BT71] W. S. Brown, 1. F. Traub, On Euclid's Algorithm and the Theory of Subre­ sultants, Journal ofACM, 18,4,505-514,1971. [C47/48] S. Chandrasekhar, On the Radiative Equilibrium of a Stellar Atmosphere, Astrophysical Journal, Pt. XXI, 106, 152-216, 1947; Pt. XXXII, 107,48- 72,1948.