Literatura-met. numeryczne

Literatura dodatkowa
(bynajmniej lista nie wyczerpuje całej dostępnej literatury a tylko podaje kilka przykładowych książek)

Podręczniki - podstawy metod numerycznych

Ȧke Bjorck, Germund Dahlquist, Metody Numeryczne, PWN, Warszawa, 1983.
Richard L. Burden, J. Douglas Faires, Numerical Analysis, Wydanie 7, Brooks/Cole, 2001.
G. Hämmerlin, K-H. Hoffmann, Numerical mathematics, Springer, New York, 1991.
J.M.Jankowscy, Metody numeryczne, tom 1, WNT, 1981.
M.Dryja, J.M.Jankowscy, Metody numeryczne, tom 2, WNT, 1982.
D.Kincaid, W.Cheney, Numerical Analysis, 2gie wyd., Brooks/Cole, 1996. (Polskie wydanie: D.Kincaid, W.Cheney, Analiza numeryczna, WNT, 2006
J. Ortega, Numerical analysis, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 2000.
A. Quarteroni, R. Sacco, F. Saleri, Numerical mathematics, Springer, New York, 2000.
Anthony Ralston Wstęp do analizy numerycznej. PWN Warszawa, 1983. Tłumaczenie I wydania z roku 1965.
Anthony Ralston, Philip Rabinowitz, A first course in numerical analysis. Reprint of the 1978 second edition. Dover Publications, Inc., Mineola, NY, 2001.
J. Stoer, R. Bulirsch, Wstęp do metod numerycznych, Tom drugi, PWN, Waszawa 1980.
J. Stoer, Wstęp do metod numerycznych, Tom pierwszy, PWN, Waszawa 1979.

Metody numeryczne algebry liniowej i metody rozwiązywania równań nieliniowych

James W. Demmel, Applied Numerical Linear Algebra. Society for Industrial and Applied Mathematics (SIAM), Philadelphia 1997.
Gene H. Golub, Charles Van Loan, Matrix Computations. Johns Hopkins University Press, 1996.
G. H. Golub, J. M. Ortega, Scientific computing, Academic Press, Boston, MA, 1993 .
G. H. Golub, J. M. Ortega, Scientific computing and differential equations, Academic Press, Boston, MA, 1992.
R. Barret, M. Berry, Tony F. Chan, J. Demmel, J. M. Donato, J. Dongarra, V. Eijkhout, R. Pozo, Ch. Romine, H. Van der Vorst,Templates for the Solution of Linear Systems. Building Blocks for Iterative Methods. On-line ftp.netlib.org/templates/templates.ps.
W. Hackbusch, Iterative solution of large sparse systems of equations, Translated and revised from the 1991 German original, Springer, New York, 1994.
C. T. Kelley, Iterative methods for linear and nonlinear equations. Frontiers in Applied Mathematics, 16. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1995.
C. T. Kelley, Solving nonlinear equations with Newton's method, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2003.
C. T. Kelley, Iterative methods for optimization, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1999.
A. Kiełbasiński, H. Schwetlick. Numeryczna algebra liniowa: wprowadzenie do obliczeń zautomatyzowanych. Wydawnictwo Naukowo Techniczne (WNT), Warszawa, 1992.
J. M. Ortega, W. C. Rheinboldt, Iterative solution of nonlinear equations in several variables, Reprint of the 1970 original, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2000.
J. M. Ortega, Numerical analysis, Second edition, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1990.
J. M. Ortega, Introduction to parallel and vector solution of linear systems, Plenum, New York, 1989.
J. M. Ortega, Matrix theory, Plenum, New York, 1987.
Beresford N. Parlett, The symmetric eigenvalue problem. Prentice-Hall Series in Computational Mathematics. Prentice-Hall, Inc., Englewood Cliffs, N.J., 1980.
Yousef Saad, Iterative methods for sparse linear systems. Society for Industrial and Applied Mathematics (SIAM), 2003. 2gie wydanie. On-line: http://www-users.cs.umn.edu/~saad/books.html
Yousef Saad, Numerical methods for large eigenvalue problems, SIAM, 2011. 2gie wydanie.On-line: http://www-users.cs.umn.edu/~saad/books.html.
A. A. Samarski, J. S. Nikołajew. Metody rozwiązywania równań siatkowych. PWN 1988.
Lloyd N. Trefethen, David Bau, III Numerical linear algebra. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1997.

Metody numeryczne dla równań różniczkowych cząstowych (i całkowych)

D. Braess, Finite elements, Translated from the 1992 German edition by Larry L. Schumaker, Third edition, Cambridge Univ. Press, Cambridge, 2007.
J. H. Bramble, Multigrid methods, Longman Sci. Tech., Harlow, 1993.
S. C. Brenner, L. R. Scott, The mathematical theory of finite element methods, 3ed edition, Springer, New York, 2008.
F. Brezzi, M. Fortin, Mixed and hybrid finite element methods, Springer, New York, 1991.
C. Canuto, Y. Hussaini, A. Quarteroni, T. Zang , Spectral methods in fluid dynamics, Springer, New York, 1988.
P. G. Ciarlet, The finite element method for elliptic problems, Reprint of the 1978 original [North-Holland, Amsterdam], Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2002.
W. Hackbusch, Integral equations, Translated and revised by the author from the 1989 German original, Birkheauser, Basel, 1995.
W. Hackbusch, Elliptic differential equations, Translated from the author's revision of the 1986 German original by Regine Fadiman and Patrick D. F. Ion, Springer, Berlin, 1992.
W. Hackbusch, Multigrid methods and applications, Springer, Berlin, 1985.
J. M. Ortega, R. G. Voigt, Solution of partial differential equations on vector and parallel computers, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1985.
J. M. Ortega, W. G. Poole, Jr., An introduction to numerical methods for differential equations, Pitman, Boston, Mass., 1981.
A. Quarteroni, F. Saleri, Scientific computing with MATLAB, Springer, Berlin, 2003.
A. Quarteroni, A. Valli, Domain decomposition methods for partial differential equations, Oxford Univ. Press, New York, 1999.
A. Quarteroni, A. Valli, Numerical approximation of partial differential equations, Springer, Berlin, 1994.
B. F. Smith, P. E. Bjorstad, W. D. Gropp, Domain decomposition, Cambridge Univ. Press, Cambridge, 1996.
Lloyd N. Trefethen, Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations, unpublished text, 1996, available at http://web.comlab.ox.ac.uk/oucl/work/nick.trefethen/pdetext.html.

Metody numeryczne dla równań różniczkowych zwyczajnych

Uri M Ascher, Linda R. Petzold, Computer methods for ordinary differential equations and differential-algebraic equations. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1998.
J.C Butcher, Numerical methods for ordinary differential equations. John Wiley & Sons, Ltd., Chichester, 2003.
K. Dekker, J. G. Verwer, Stability of Runge-Kutta methods for stiff nonlinear differential equations. CWI Monographs, 2. North-Holland Publishing Co., Amsterdam, 1984.
C. William Gear, Numerical initial value problems in ordinary differential equations. Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971.
Ernst Hairer, S.P. Nørsett, G. Wanner, Solving ordinary differential equations. I. Nonstiff problems. Second edition. Springer Series in Computational Mathematics, 8. Springer-Verlag, Berlin, 1993.
Ernst Hairer, G. Wanner Solving ordinary differential equations. II. Stiff and differential-algebraic problems. Second edition. Springer Series in Computational Mathematics, 14. Springer-Verlag, Berlin, 1996.
Ernst Hairer, Christian Lubich, Michael Roche, The numerical solution of differential-algebraic systems by Runge-Kutta methods. Lecture Notes in Mathematics, 1409. Springer-Verlag, Berlin, 1989.
Peter Henrici, Discrete variable methods in ordinary differential equations. John Wiley & Sons, Inc., New York-London 1962.
Herbert B. Keller, Numerical solution of two point boundary value problems. Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1976
J. D. Lambert, Numerical methods for ordinary differential systems. The initial value problem. John Wiley & Sons, Ltd., Chichester, 1991.
Leon Lapidus, John H. Seinfeld, Numerical solution of ordinary differential equations. Mathematics in Science and Engineering, Vol. 74 Academic Press, New York-London 1971
Andrzej Palczewski Równania Różniczkowe zwyczajne Teoria i metody numeryczne z wykorzystaniem komputerowego systemu obliczeń symbolicznych. Wydawnictwo Naukowo-Techniczne (WNT) ,Warszawa 1999.
Lawrence F. Shampine, Numerical solution of ordinary differential equations. Chapman & Hall, New York, 1994.
Lawrence F. Shampine, C. William Gear, A user's view of solving stiff ordinary differential equations. SIAM Review 21 (1979), nr. 1, 1--17.
Hans J. Stetter, Analysis of discretization methods for ordinary differential equations. Springer Tracts in Natural Philosophy, Vol. 23. Springer-Verlag, New York-Heidelberg, 1973.
Lloyd N. Trefethen, Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations, unpublished text, 1996, available at http://web.comlab.ox.ac.uk/oucl/work/nick.trefethen/pdetext.html.

Teoria aproksymacja - funkcje gięte: splajny

Arcangéli, Rémi; López de Silanes, María Cruz; Torrens, Juan José. Multidimensional minimizing splines. Theory and applications. Grenoble Sciences. Kluwer Academic Publishers, Boston, MA, 2004.
Bezhaev, Anatoly Yu., Vasilenko, Vladimir A. Variational theory of splines. Kluwer Academic/Plenum Publishers, New York, 2001.
Carl de Boor,A practical guide to splines. Applied Mathematical Sciences, 27.
Lai, Ming-Jun, Schumaker, Larry L. Spline functions on triangulations. Encyclopedia of Mathematics and its Applications, 110. Cambridge University Press, Cambridge, 2007
Prautzsch, Hartmut, Boehm, Wolfgang, Paluszny, Marco. Bézier and B-spline techniques. Mathematics and Visualization. Springer-Verlag, Berlin, 2002.
P. M. Prenter, P. M. Splines and variational methods. Reprint of the 1975 original. Wiley Classics Library. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1989.
Schumaker, Larry L. Spline functions: basic theory. Third edition. Cambridge Mathematical Library. Cambridge University Press, Cambridge, 2007.
Wang, Ren-Hong. Multivariate spline functions and their applications. Translated from the 1994 Chinese original by Shao-Ming Wang and revised by the author. Mathematics and its Applications, 529. Kluwer Academic Publishers, Dordrecht; Science Press, Beijing, 2001.

Szybka transformacja Fouriera

Clausen, Michael,Baum, Ulrich. Fast Fourier transforms. (English summary) Bibliographisches Institut, Mannheim, 1993.
Nussbaumer, Henri J. Fast Fourier transform and convolution algorithms. Springer Series in Information Sciences, 2. Springer-Verlag, Berlin-New York, 1981.
Pickering, Morgan. An introduction to fast Fourier transform methods for partial differential equations, with applications. Electronic & Electrical Engineering Research Studies: Applied and Engineering Mathematics Series, 4. Research Studies Press, Ltd., Chichester; John Wiley & Sons, Inc., New York, 1986.
Richard Tolimieri, Myoung An, Chao Lu, Mathematics of multidimensional Fourier transform algorithms. Second edition. Signal Processing and Digital Filtering. Springer-Verlag, New York, 1997.
Charles Van Loan, Computational frameworks for the fast Fourier transform. Frontiers in Applied Mathematics, 10. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992.
Walker, James S. Fast Fourier transforms. Second edition. Studies in Advanced Mathematics. CRC Press, Boca Raton, FL, 1996.

Handbook of numerical analysis. (Encyklopedia analizy numerycznej- zbiór artykułów opisujących wszystkie działy)

Handbook of numerical analysis. Vol. I. Edited by P. G. Ciarlet and J.-L. Lions. North-Holland, Amsterdam, 1990. Contents: P. G. Ciarlet and J.-L. Lions, General preface (pp. v--vi). Finite difference methods. Part 1: G. I. Marchuk, Introduction (pp. 3--4); Vidar Thomée, Finite difference methods for linear parabolic equations (pp. 5--196); G. I. Marchuk, Splitting and alternating direction methods (pp. 197--462). Solution of equations in $R^n$. Part 1: Åke Björck, Least squares methods (pp. 465--652).
Handbook of numerical analysis. Vol. II. Finite element methods. Part 1. Edited by P. G. Ciarlet and J.-L. Lions. North-Holland, Amsterdam, 1991. Contents: J. Tinsley Oden, Finite elements: an introduction (pp. 3--15); P. G. Ciarlet, Basic error estimates for elliptic problems (pp. 17--351); Lars B. Wahlbin, Local behavior in finite element methods (pp. 353--522); J. E. Roberts [Jean Elizabeth Roberts] and J.-M. Thomas [Jean-Marie Thomas], Mixed and hybrid methods (pp. 523--639); I. Babuv ska and J. Osborn [John E. Osborn], Eigenvalue problems (pp. 641--787); Hiroshi Fujita and Takashi Suzuki, Evolution problems (pp. 789--928).
Handbook of numerical analysis. Vol. III. Techniques of scientific computing. Part 1. Numerical methods for solids. Part 1. Solution of equations in R^n. Part 2. Edited by P. G. Ciarlet and J.-L. Lions. North-Holland, Amsterdam, 1994. Contents: Claude Brezinski, Historical perspective on interpolation, approximation and quadrature (3--46); Claude Brezinski and Jeannette Van Iseghem, Padé approximations (47--222); Blagovest Sendov and Andreui Andreev, Approximation and interpolation theory (223--462); Patrick Le Tallec, Numerical methods for nonlinear three-dimensional elasticity (465--622); Bl. Sendov, A. Andreev [Andreui St. Andreev] and N. Kjurkchiev [Nikolaui V. Kyurkchiev], Numerical solution of polynomial equations (625--778).
Handbook of numerical analysis. Vol. IV. Finite element methods. Part 2. Numerical methods for solids. Part 2. Edited by P. G. Ciarlet and J. L. Lions. North-Holland, Amsterdam, 1996. Contents: O. C. Zienkiewicz, Origins, milestones and directions of the finite element method---a personal view (3--67); P. L. George, Automatic mesh generation and finite element computation (69--190); Edmund Christiansen, Limit analysis of collapse states (193--312); J. Haslinger, I. Hlavácek and J. Necas, Numerical methods for unilateral problems in solid mechanics (313--485); L. Trabucho and J. M. Via no [Juan M. Via no Rey], Mathematical modelling of rods (487--974).
Handbook of numerical analysis. Vol. V. Techniques of scientific computing. Part 2. Edited by P. G. Ciarlet and J. L. Lions. North-Holland, Amsterdam, 1997. Contents: Eugene L. Allgower and Kurt Georg, Numerical path following (3--207); Christine Bernardi and Yvon Maday, Spectral methods (209--485); Gabriel Caloz and Jacques Rappaz, Numerical analysis for nonlinear and bifurcation problems (487--637); Y. Meyer, Wavelets and fast numerical algorithms (639--713); Jean-Jacques Risler, Computer aided geometric design (715--818).
Handbook of numerical analysis. Vol. VI. 1998. Numerical methods for solids. Part 3. Numerical methods for fluids. Part 1. Edited by P. G. Ciarlet and J. L. Lions. North-Holland, Amsterdam, Contents: Robert M. Ferencz and Thomas J. R. Hughes, Iterative finite element solutions in nonlinear solid mechanics (3--178); Thomas J. R. Hughes and David M. Barnett, Obituary: Juan Carlos Simo (1952--1994) (179--181); J. C. Simo, Numerical analysis and simulation of plasticity (183--499); Martine Marion and Roger Temam, Navier-Stokes equations: theory and approximation (503--688).
Handbook of numerical analysis. Vol. VII. Solution of equations in R^n. Part 3. Techniques of scientific computing. Part 3. Edited by P. G. Ciarlet and J. L. Lions. North-Holland, Amsterdam, 2000. Contents: Gérard Meurant, Gaussian elimination for the solution of linear systems of equations (3--170); James H. Bramble and Xuejun Zhang, The analysis of multigrid methods (173--415); Albert Cohen, Wavelet methods in numerical analysis (417--711); Robert Eymard, Thierry Gallouët and Raphaèle Herbin, Finite volume methods (713--1020).
Handbook of numerical analysis. Vol. VIII. Solution of equations in R^n. Part 4. Techniques of scientific computing. Part 4. Numerical methods for fluids. Part 2. Edited by P. G. Ciarlet and J. L. Lions. North-Holland, Amsterdam, 2002. Contents: Henk A. van der Vorst, Computational methods for large eigenvalue problems (3--179); Patrick J. Rabier and Werner C. Rheinboldt, Theoretical and numerical analysis of differential-algebraic equations (183--540); E. Fernández-Cara, F. Guillén [Francisco M. Guillén González] and R. R. Ortega, Mathematical modeling and analysis of viscoelastic fluids of the Oldroyd kind (543--661).
Handbook of numerical analysis. Vol. IX. Numerical methods for fluids. Part 3. Edited by P. G. Ciarlet and J. L. Lions. North-Holland, Amsterdam, 2003. Contents: Roland Glowinski, Finite element methods for incompressible viscous flow (3--1176)