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Book Cover
PRINTED BOOKS
Author Mayers, D. F. (David Francis), 1931-

Title An introduction to numerical analysis / David Mayers and Endre Süli.

Published Cambridge : Cambridge University Press, 2002.

Copies

Location Call No. Status
 UniM ERC  518 MAYE    AVAILABLE
Physical description x, 433 pages ; 23cm
Notes Includes index.
Contents 1 Solution of equations by iteration 1 -- 1.2 Simple iteration 2 -- 1.3 Iterative solution of equations 17 -- 1.4 Relaxation and Newton's method 19 -- 1.5 Secant method 25 -- 1.6 Bisection method 28 -- 1.7 Global behaviour 29 -- 2 Solution of systems of linear equations 39 -- 2.2 Gaussian elimination 44 -- 2.3 LU factorisation 48 -- 2.4 Pivoting 52 -- 2.5 Solution of systems of equations 55 -- 2.6 Computational work 56 -- 2.7 Norms and condition numbers 58 -- 2.8 Hilbert matrix 72 -- 2.9 Least squares method 74 -- 3 Special matrices 87 -- 3.2 Symmetric positive definite matrices 87 -- 3.3 Tridiagonal and band matrices 93 -- 3.4 Monotone matrices 98 -- 4 Simultaneous nonlinear equations 104 -- 4.2 Simultaneous iteration 106 -- 4.3 Relaxation and Newton's method 116 -- 4.4 Global convergence 123 -- 5 Eigenvalues and eigenvectors of a symmetric matrix 133 -- 5.2 Characteristic polynomial 137 -- 5.3 Jacobi's method 137 -- 5.4 Gerschgorin theorems 145 -- 5.5 Householder's method 150 -- 5.6 Eigenvalues of a tridiagonal matrix 156 -- 5.7 QR algorithm 162 -- 5.8 Inverse iteration for the eigenvectors 166 -- 5.9 Rayleigh quotient 170 -- 5.10 Perturbation analysis 172 -- 6 Polynomial interpolation 179 -- 6.2 Lagrange interpolation 180 -- 6.3 Convergence 185 -- 6.4 Hermite interpolation 187 -- 6.5 Differentiation 191 -- 7 Numerical integration-I 200 -- 7.2 Newton-Cotes formulae 201 -- 7.3 Error estimates 204 -- 7.4 Runge phenomenon revisited 208 -- 7.5 Composite formulae 209 -- 7.6 Euler-Maclaurin expansion 211 -- 7.7 Extrapolation methods 215 -- 8 Polynomial approximation in the [infinity]-norm 224 -- 8.2 Normed linear spaces 224 -- 8.3 Best approximation in the [infinity]-norm 228 -- 8.4 Chebyshev polynomials 241 -- 8.5 Interpolation 244 -- 9 Approximation in the 2-norm 252 -- 9.2 Inner product spaces 253 -- 9.3 Best approximation in the 2-norm 256 -- 9.4 Orthogonal polynomials 259 -- 9.5 Comparisons 270 -- 10 Numerical integration - II 277 -- 10.2 Construction of Gauss quadrature rules 277 -- 10.3 Direct construction 280 -- 10.4 Error estimation for Gauss quadrature 282 -- 10.5 Composite Gauss formulae 285 -- 10.6 Radau and Lobatto quadrature 287 -- 11 Piecewise polynomial approximation 292 -- 11.2 Linear interpolating splines 293 -- 11.3 Basis functions for the linear spline 297 -- 11.4 Cubic splines 298 -- 11.5 Hermite cubic splines 300 -- 11.6 Basis functions for cubic splines 302 -- 12 Initial value problems for ODEs 310 -- 12.2 One-step methods 317 -- 12.3 Consistency and convergence 321 -- 12.4 An implicit one-step method 324 -- 12.5 Runge-Kutta methods 325 -- 12.6 Linear multistep methods 329 -- 12.7 Zero-stability 331 -- 12.8 Consistency 337 -- 12.9 Dahlquist's theorems 340 -- 12.10 Systems of equations 341 -- 12.11 Stiff systems 343 -- 12.12 Implicit Runge-Kutta methods 349 -- 13 Boundary value problems for ODEs 361 -- 13.2 A model problem 361 -- 13.3 Error analysis 364 -- 13.4 Boundary conditions involving a derivative 367 -- 13.5 General self-adjoint problem 370 -- 13.6 Sturm-Liouville eigenvalue problem 373 -- 13.7 Shooting method 375 -- 14 Finite element method 385 -- 14.1 Introduction: the model problem 385 -- 14.2 Rayleigh-Ritz and Galerkin principles 388 -- 14.3 Formulation of the finite element method 391 -- 14.4 Error analysis of the finite element method 397 -- 14.5 A posteriori error analysis by duality 403 -- Appendix A An overview of results from real analysis 419 -- Appendix B WWW-resources 423.
Summary Numerical analysis provides the theoretical foundation for the numerical algorithms we rely on to solve a multitude of computational problems in science. Based on a successful course at Oxford University, this book covers a wide range of such problems from the approximation of functions and integrals to the approximate solution of algebraic, transcendental, differential and integral equations. Throughout the book, particular attention is paid to the essential qualities of a numerical algorithm-stability, accuracy, reliability and efficiency.
The authors go further than simply providing recipes for solving computational problems. They carefully analyse the reasons why methods might fail to give accurate answers, or why one method might return an answer in seconds while another would take billions of years. This book is ideal as a text for students in the second year of a university mathematics course. It combines practicality regarding applications with consistently high standards of rigour.
Other author Süli, Endre, 1956-
Subject Numerical analysis.
ISBN 0521810264 : £55.00
0521007941 paperback £19.95