Introduction to Numerical Analysis
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in re search and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numeri cal and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathe matical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs.
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algorithm approximation arbitrary arithmetic B-splines boundary-value problem characteristic polynomial Choleski coefficients column compute condition convergence decomposition defined denote determined diagonal differential equations eigenvalues eigenvectors elements Euler's method exact solution example finite floating-point formula function f given Hermite interpolation Hermitian Hessenberg matrix initial-value problem integration interval iterative methods Jacobi method Jordan normal form linear equations lub(A multistep method n x n matrix Newton's method nonsingular norm numerically stable obtained orthogonal parameters positive definite PROOF QR method recursion roots roundoff errors SA(Y satisfies Section sequence shooting method solving spline function step stepsize system of equations Theorem transformation triangular matrix tridiagonal tridiagonal matrix unique unitary unitary matrix upper triangular vector y(ac zero