Introduction to Numerical Analysis, 3/e

This book contains a large amount of information not found in standard textbooks. Written for the advanced undergraduate/beginning graduate student, it combines the modern mathematical standards of numerical analysis with an understanding of the needs of the computer scientist working on practical applications. Among its many particular features are: fully worked-out examples; many carefully selected and formulated problems; fast Fourier transform methods; a thorough discussion of some important minimization methods; solution of stiff or implicit ordinary differential equations and of differential algebraic systems; modern shooting techniques for solving two-point boundary value problems; and basics of multigrid methods. This new edition features expanded presentation of Hermite interpolation and B-splines, with a new section on multi-resolution methods and B-splines. New material on differential equations and the iterative solution of linear equations include: solving differential equations in the presence of discontinuities whose locations are not known at the outset; techniques for sensitivity analyses of differential equations dependent on additional parameters; new advanced techniques in multiple shooting; and Krylov space methods for non-symmetric systems of linear equations.

TABLE OF CONTENTS

Error Analysis * Interpolation * Topics of Integration * Systems of Linear Equations * Finding Zeros and Minimum Points by Iterative Methods * Eigenvalue Problems * Ordinary Differential Equations * Iterative Methods for the Solution of Large Systems of Linear Equations * General Literature on Numerical Methods

這本書包含了許多標準教科書中找不到的大量資訊。針對高年級本科生和初級研究生寫作，它結合了現代數值分析的數學標準和對從事實際應用的計算機科學家的需求的理解。它的許多特點包括：完整的實例解析；許多精心選擇和構思的問題；快速傅立葉變換方法；對一些重要的最小化方法的詳細討論；解決嚴格或隱式常微分方程和微分代數系統；用於解決兩點邊界值問題的現代射擊技術；以及多重網格方法的基礎知識。這個新版本增加了埃爾米特插值和B樣条的介紹，並新增了關於多分辨率方法和B樣条的部分。關於微分方程和線性方程的迭代解法的新材料包括：在不知道起始位置的不連續性存在下解決微分方程；對依賴於額外參數的微分方程進行敏感性分析的技術；多重射擊的新高級技術；以及非對稱線性方程系統的Krylov空間方法。

目錄：
- 誤差分析
- 插值
- 積分的主題
- 線性方程組
- 通過迭代方法找到零點和最小點
- 特徵值問題
- 常微分方程
- 解決大型線性方程組的迭代方法
- 數值方法的一般文獻