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The Bibliography Referenced Books [Ach92] N. I. Achieser. Theory of Approximation. Dover Publications Inc., New York, 1992. Reprint of the 1956 English translation of the 1st Rus- sian edition; the 2nd augmented Russian edition is available, Moscow, Nauka, 1965. [AH05] Kendall Atkinson and Weimin Han. Theoretical Numerical Analysis: A Functional Analysis Framework, volume 39 of Texts in Applied Mathe- matics. Springer, New York, second edition, 2005. [Atk89] Kendall E. Atkinson. An Introduction to Numerical Analysis. John Wiley & Sons Inc., New York, second edition, 1989. [Axe94] Owe Axelsson. Iterative Solution Methods. Cambridge University Press, Cambridge, 1994. [Bab86] K. I. Babenko. Foundations of Numerical Analysis [Osnovy chislennogo analiza]. Nauka, Moscow, 1986. [Russian]. [BD92] C. A. Brebbia and J. Dominguez. Boundary Elements: An Introductory Course. Computational Mechanics Publications, Southampton, second edition, 1992. [Ber52] S. N. Bernstein. Collected Works. Vol. I. The Constructive Theory of Functions [1905–1930]. Izdat. Akad. Nauk SSSR, Moscow, 1952. [Russian]. [Ber54] S. N. Bernstein. Collected Works. Vol. II. The Constructive Theory of Functions [1931–1953]. Izdat. Akad. Nauk SSSR, Moscow, 1954. [Russian]. [BH02] K. Binder and D. W. Heermann. Monte Carlo Simulation in Statistical Physics: An Introduction, volume 80 of Springer Series in Solid-State Sciences. Springer-Verlag, Berlin, fourth edition, 2002. [BHM00] William L. Briggs, Van Emden Henson, and Steve F. McCormick. A Multigrid Tutorial. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, second edition, 2000. [Boy01] John P. Boyd. Chebyshev and Fourier Spectral Methods. Dover Publi- cations Inc., Mineola, NY, second edition, 2001. [Bra84] Achi Brandt. Multigrid Techniques: 1984 Guide with Applications to Fluid Dynamics, volume 85 of GMD-Studien [GMD Studies]. 509 510 Referenced Books Gesellschaft f¨ur Mathematik und Datenverarbeitung mbH, St. Augustin, 1984. [Bra93] James H. Bramble. Multigrid Methods, volume 294 of Pitman Research Notes in Mathematics Series. Longman Scientific & Technical, Harlow, 1993. [BS02] Susanne C. Brenner and L. Ridgway Scott. The Mathematical Theory of Finite Element Methods, volume 15 of Texts in Applied Mathematics. Springer-Verlag, New York, second edition, 2002. [But03] J. C. Butcher. Numerical Methods for Ordinary Differential Equations. John Wiley & Sons Ltd., Chichester, 2003. [CdB80] Samuel Conte and Carl de Boor. Elementary Numerical Analysis: An Algorithmic Approach. McGraw-Hill, New York, third edition, 1980. [CH06] Alexandre J. Chorin and Ole H. Hald. Stochastic Tools in Mathematics and Science, volume 1 of Surveys and Tutorials in the Applied Mathe- matical Sciences. Springer, New York, 2006. [Che66] E. W. Cheney. Introduction to Approximation Theory. International Series in Pure and Applied Mathematics. McGraw-Hill Book Company, New York, 1966. [CHQZ88] Claudio Canuto, M. Yousuff Hussaini, Alfio Quarteroni, and Thomas A. Zang. Spectral Methods in Fluid Dynamics. Springer Series in Compu- tational Physics. Springer-Verlag, New York, 1988. [CHQZ06] Claudio Canuto, M. Yousuff Hussaini, Alfio Quarteroni, and Thomas A. Zang. Spectral Methods. Fundamentals in Single Domains. Springer Series in Scientific Computation. Springer-Verlag, New York, 2006. [Cia02] Philippe G. Ciarlet. The Finite Element Method for Elliptic Problems, volume 40 of Classics in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2002. Reprint of the 1978 original [North-Holland, Amsterdam; MR0520174 (58 #25001)]. [dB01] Carl de Boor. A Practical Guide to Splines, volume 27 of Applied Math- ematical Sciences. Springer-Verlag, New York, revised edition, 2001. [DB03] Germund Dahlquist and Ake Bj¨orck. Numerical Methods. Dover Pub- lications Inc., Mineola, NY, 2003. Translated from the Swedish by Ned Anderson, Reprint of the 1974 English translation. [Dem06] Leszek Demkowicz. Computing with hp-Adaptive Finite Elements. I. One- and Two-Dimensional Elliptic and Maxwell Problems.Taylor& Francis, Boca Raton, 2006. [D¨or82] Heinrich D¨orrie. 100 Great Problems of Elementary Mathematics. Dover Publications Inc., New York, 1982. Their history and solution, Referenced Books 511 Reprint of the 1965 edition, Translated from the fifth edition of the Ger- man original by David Antin. [DR84] Philip J. Davis and Philip Rabinowitz. Methods of Numerical Integra- tion. Computer Science and Applied Mathematics. Academic Press Inc., Orlando, FL, second edition, 1984. [D’y96] Eugene G. D’yakonov. Optimization in Solving Elliptic Problems. CRC Press, Boca Raton, FL, 1996. Translated from the 1989 Russian origi- nal, Translation edited and with a preface by Steve McCormick. [Fed77] M. V. Fedoryuk. The Saddle-Point Method [Metod perevala]. Nauka, Moscow, 1977. [Russian]. [FM87] L. Fox and D. F. Mayers. Numerical Solution of Ordinary Differential Equations. Chapman & Hall, London, 1987. [GAKK93] S. K. Godunov, A. G. Antonov, O. P. Kiriljuk, and V. I. Kostin. Guar- anteed Accuracy in Numerical Linear Algebra, volume 252 of Mathe- matics and its Applications. Kluwer Academic Publishers Group, Dor- drecht, 1993. Translated and revised from the 1988 Russian original. [Gan59] F. R. Gantmacher. The Theory of Matrices. Vols. 1, 2. Translated by K. A. Hirsch. Chelsea Publishing Co., New York, 1959. [GKO95] Bertil Gustafsson, Heinz-Otto Kreiss, and Joseph Oliger. Time Depen- dent Problems and Difference Methods. Pure and Applied Mathemat- ics (New York). John Wiley & Sons Inc., New York, 1995. A Wiley- Interscience Publication. [GL81] Alan George and Joseph W. H. Liu. Computer Solution of Large Sparse Positive Definite Systems. Prentice-Hall Inc., Englewood Cliffs, N.J., 1981. Prentice-Hall Series in Computational Mathematics. [Gla04] Paul Glasserman. Monte Carlo Methods in Financial Engineering,vol- ume 53 of Applications of Mathematics (New York). Springer-Verlag, New York, 2004. Stochastic Modelling and Applied Probability. [GO77] David Gottlieb and Steven A. Orszag. Numerical Analysis of Spectral Methods: Theory and Applications. Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1977. CBMS-NSF Regional Confer- ence Series in Applied Mathematics, No. 26. [GR64] S. K. Godunov and V. S. Ryabenki. Theory of Difference Schemes. An Introduction. Translated by E. Godfredsen. North-Holland Publishing Co., Amsterdam, 1964. [GR87] S. K. Godunov and V. S. Ryaben’kii. Difference schemes: An intro- duction to the underlying theory, volume 19 of Studies in Mathematics and its Applications. North-Holland Publishing Co., Amsterdam, 1987. Translated from the Russian by E. M. Gelbard. 512 Referenced Books [GVL89] Gene H. Golub and Charles F. Van Loan. Matrix Computations,vol- ume 3 of Johns Hopkins Series in the Mathematical Sciences. Johns Hopkins University Press, Baltimore, MD, second edition, 1989. [Hac85] Wolfgang Hackbusch. Multigrid Methods and Applications, volume 4 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin, 1985. [Hal94] W. S. Hall. The Boundary Element Method, volume 27 of Solid Me- chanics and its Applications. Kluwer Academic Publishers Group, Dor- drecht, 1994. [Hen64] Peter Henrici. Elements of Numerical Analysis. John Wiley & Sons Inc., New York, 1964. [HGG06] Jan S. Hesthaven, Sigal Gottlieb, and David Gottlieb. Spectral Meth- ods for Time-Dependent Problems. Cambridge University Press, Cam- bridge, 2006. [HJ85] Roger A. Horn and Charles R. Johnson. Matrix Analysis. Cambridge University Press, Cambridge, 1985. [HNW93] E. Hairer, S. P. Nørsett, and G. Wanner. Solving Ordinary Differential Equations I: Nonstiff Problems, volume 8 of Springer Series in Compu- tational Mathematics. Springer-Verlag, Berlin, second edition, 1993. [HW96] E. Hairer and G. Wanner. Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, volume 14 of Springer Se- ries in Computational Mathematics. Springer-Verlag, Berlin, second edition, 1996. [IK66] Eugene Isaacson and Herbert Bishop Keller. Analysis of Numerical Methods. John Wiley & Sons Inc., New York, 1966. [Jac94] Dunham Jackson. The Theory of Approximation, volume 11 of Ameri- can Mathematical Society Colloquium Publications. American Mathe- matical Society, Providence, RI, 1994. Reprint of the 1930 original. [KA82] L. V. Kantorovich and G. P. Akilov. Functional Analysis.Pergamon Press, Oxford, second edition, 1982. Translated from the Russian by Howard L. Silcock. [Kel95] C. T. Kelley. Iterative Methods for Linear and Nonlinear Equations, volume 16 of Frontiers in Applied Mathematics. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1995. With sepa- rately available software. [Kel03] C. T. Kelley. Solving Nonlinear Equations with Newton’s Method. Fun- damentals of Algorithms. Society for Industrial and Applied Mathemat- ics (SIAM), Philadelphia, PA, 2003. Referenced Books 513 [KF75] A. N. Kolmogorov and S. V. Fomin. Introductory Real Analysis. Dover Publications Inc., New York, 1975. Translated from the second Russian edition and edited by Richard A. Silverman, Corrected reprinting. [Lad69] O. A. Ladyzhenskaya. The Mathematical Theory of Viscous Incom- pressible Flow. Second English edition, revised and enlarged. Trans- lated from the Russian by Richard A. Silverman and John Chu. Math- ematics and its Applications, Vol. 2. Gordon and Breach Science Pub- lishers, New York, 1969. [LeV02] Randall J. LeVeque. Finite Volume Methods for Hyperbolic Problems. Cambridge Texts in Applied Mathematics. Cambridge
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