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An Introduction to Numerical Analysis
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By Endre Süli, David F. Mayers, * Publisher: Cambridge University Press * Number Of Pages: 444 * Publication Date: 2003-09-08 * Sales Rank: 755940 * ISBN / ASIN: 0521007941 * EAN: 9780521007948 * Binding: Paperback * Manufacturer: Cambridge University Press * Studio: Cambridge University Press * Average Rating: 4.5 * Total Reviews: 2 Review: Numerical analysis focusing on foundation This book has emphasis on analysis of numerical methods, including error bound, consistency, convergence, stability. In most cases, a numerical method is introduced, followed by analysis and proofs. For engineering students, who like to know more algorithms and a little bit of analysis, this book may not be the best choice. Although this book is mainly about analysis, it does include clear presentation of many numerical methods, including topics in nonlinear equations solving, numerical linear algebra, polynomial interpolation and integration, numerical solution of ODE. In numerical linear algebra, it includes LU factorization with pivoting, Gerschgorin's theorem of eigenvalue positions, Calculating eigenvalues by Jacobi plane rotation, Householder tridiagonalization, Sturm sequence property for tridiagonal symmetric matrix. Interpolation includes Lagrange polynomial, Hermite polynomial, Newton-Cotes integration, Improved Trapezium integration through Romberg method, Oscillation theorem for minimax approximation, Chebyshev polynomial, least square polynomial approximation to a known function, Gauss quadrature using Hermite polynomial, Piecewise linear/cubic splines. Ordinary ddifferential equations section includes initial value problems with one-step and multiple steps, boundary value problems using finite difference and shooting method, Galerkin finite element method. The book gives basic definitions including norms, matrix condition numbers, real symmetric positive definite matrix, Rayleigh quotient, orthogonal polynomials, stiffness, Sobolev space. One place that is not clear is about QR algorithm for tridiagonal matrix. In summary, the book is written clearly. Every numerical method is presented based on mathematics. There are many proofs (there is one proof with more than 3 pages), most of them that I decided to read are pretty easy to follow. There are not much implementation details and tricks. But this book will tell you when a method will converge and when a method is better. As a non-math major reader, I wish it could present more algorithms, such as algorithms for eigenvalues of nonsymmetric matrix, more details in finite difference method, a little bit of partial differential equations etc. 注：论坛有一本Introduction to Numerical Analysis 但此书没有具体相关信息，故无法判断是否重复，若重复，请版主删除！ [ Last edited by skyflyzw on 2007-8-30 at 22:23 ] |
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