Analysis of Numerical MethodsCourier Corporation, 26 avr. 2012 - 576 pages In this age of omnipresent digital computers and their capacity for implementing numerical methods, no applied mathematician, physical scientist, or engineer can be considered properly trained without some understanding of those methods. This text, suitable for advanced undergraduate and graduate-level courses, supplies the required knowledge — not just by listing and describing methods, but by analyzing them carefully and stressing techniques for developing new methods. Based on each author's more than 40 years of experience in teaching university courses, this book offers lucid, carefully presented coverage of norms, numerical solution of linear systems and matrix factoring, iterative solutions of nonlinear equations, eigenvalues and eigenvectors, polynomial approximation, numerical solution of differential equations, and more. No mathematical preparation beyond advanced calculus and elementary linear algebra (or matrix theory) is assumed. Examples and problems are given that extend or amplify the analysis in many cases. |
Autres éditions - Tout afficher
Analysis of Numerical Methods, Volume 10 Eugene Isaacson,Herbert Bishop Keller Affichage d'extraits - 1966 |
Expressions et termes fréquents
applied approximation assume bound Chapter coefficients column computed constant continuous function convergence corollary corresponding defined definition degree of precision determined difference equations difference scheme differential equation distinct points divided difference domain of dependence eigenvalues eigenvectors elements evaluation fact factor finite follows function f(x Gaussian elimination Gaussian quadrature given Hence Hint implies inequality initial value initial value problem integral interpolation polynomial interval iterative methods Lemma linear matrix norm maximum Newton-Cotes formulae nodes non-singular notation obtained operations orthogonal orthonormal Pn(x polynomial of degree procedure Proof quadrature formulae recursion result root roundoff error satisfy Section sequence ſº solve Subsection symmetric symmetric matrix Taylor's theorem Theorem theory triangular trigonometric sum truncation error unique value problem vanishes variable vector vector norm Verify well-posed yields zero