Numerical analysis: mathematics of scientific computing Third Edition = 数值分析 (英文版·第3版)PDF电子书下载
- 电子书积分:21 积分如何计算积分?
- 作 者:David Kincaid ; Ward Cheney
- 出 版 社:China Machine Press
- 出版年份:2003
- ISBN:7111119134
- 页数:794 页
Numerical Analysis:What Is It? 1
1 Mathematical Preliminaries 3
1.0 Introduction 3
1.1 Basic Concepts and Taylor’s Theorem 3
1.2 Orders of Convergence and Additional Basic Concepts 15
1.3 Difference Equations 28
2 Computer Arithmetic 37
2.0 Introduction 37
2.1 Floating-Point Numbers and Roundoff Errors 37
2.2 Absolute and Relative Errors:Loss of Significance 55
2.3 Stable and Unstable Computations:Conditioning 64
3 Solution of Nonlinear Equations 73
3.0 Introduction 73
3.1 Bisection (Interval Halving) Method 74
3.2 Newton’s Method 81
3.3 Secant Method 93
3.4 Fixed Points and Functional Iteration 100
3.5 Computing Roots of Polynomials 109
3.6 Homotopy and Continuation Methods 130
4 Solving Systems of Linear Equations 139
4.0 Introduction 139
4.1 Matrix Algebra 140
4.2 LU and Cholesky Factorizations 149
4.3 Pivoting and Constructing an Algorithm 163
4.4 Norms and the Analysis of Errors 186
4.5 Neumann Series and Iterative Refinement 197
4.6 Solution of Equations by Iterative Methods 207
4.7 Steepest Descent and Conjugate Gradient Methods 232
4.8 Analysis of Roundoff Error in the Gaussian Algorithm 245
5 Selected Topics in Numerical Linear Algebra 254
5.0 Review of Basic Concepts 254
5.1 Matrix Eigenvalue Problem:Power Method 257
5.2 Schur’s and Gershgorin’s Theorems 265
5.3 Orthogonal Factorizations and Least-Squares Problems 273
5.4 Singular-Value Decomposition and Pseudoinverses 287
5.5 QR-Algorithm of Francis for the Eigenvalue Problem 298
6 Approximating Functions 308
6.0 Introduction 308
6.1 Polynomial Interpolation 308
6.2 Divided Differences 327
6.3 Hermite Interpolation 338
6.4 Spline Interpolation 349
6.5 B-Splines:Basic Theory 366
6.6 B-Splines:Applications 377
6.7 Taylor Series 388
6.8 Best Approximation:Least-Squares Theory 392
6.9 Best Approximation:Chebyshev Theory 405
6.10 Interpolation in Higher Dimensions 420
6.11 Continued Fractions 438
6.12 Trigonometric Interpolation 445
6.13 Fast Fourier Transform 451
6.14 Adaptive Approximation 460
7 Numerical Differentiation and Integration 465
7.1 Numerical Differentiation and Richardson Extrapolation 465
7.2 Numerical Integration Based on Interpolation 478
7.3 Gaussian Quadrature 492
7.4 Romberg Integration 502
7.5 Adaptive Quadrature 507
7.6 Sard’s Theory of Approximating Functionals 513
7.7 Bernoulli Polynomials and the Euler-Maclaurin Formula 519
8 Numerical Solution of Ordinary Differential Equations 524
8.0 Introduction 524
8.1 The Existence and Uniqueness of Solutions 524
8.2 Taylor-Series Method 530
8.3 Runge-Kutta Methods 539
8.4 Multistep Methods 549
8.5 Local and Global Errors:Stability 557
8.6 Systems and Higher-Order Ordinary Differential Equations 565
8.7 Boundary-Value Problems 572
8.8 Boundary-Value Problems:Shooting Methods 581
8.9 Boundary-Value Problems:Finite-Differences 589
8.10 Boundary-Value Problems:Collocation 593
8.11 Linear Differential Equations 597
8.12 Stiff Equations 608
9 Numerical Solution of Partial Differential Equations 615
9.0 Introduction 615
9.1 Parabolic Equations:Explicit Methods 615
9.2 Parabolic Equations:Implicit Methods 623
9.3 Problems Without Time Dependence:Finite-Differences 629
9.4 Problems Without Time Dependence:Galerkin Methods 634
9.5 First-Order Partial Differential Equations:Characteristics 642
9.6 Quasilinear Second-Order Equations:Characteristics 650
9.7 Other Methods for Hyperbolic Problems 660
9.8 Multigrid Method 667
9.9 Fast Methods for Poisson’s Equation 676
10 Linear Programming and Related Topics 681
10.1 Convexity and Linear Inequalities 681
10.2 Linear Inequalities 689
10.3 Linear Programming 695
10.4 The Simplex Algorithm 700
11 Optimization 711
11.0 Introduction 711
11.1 One-Variable Case 712
11.2 Descent Methods 716
11.3 Analysis of Quadratic Objective Functions 719
11.4 Quadratic-Fitting Algorithms 721
11.5 Nelder-Meade Algorithm 722
11.6 Simulated Annealing 723
11.7 Genetic Algorithms 724
11.8 Convex Programming 725
11.9 Constrained Minimization 726
11.10 Pareto Optimization 727
Appendix A An Overview of Mathematical Software 731
Bibliography 745
Index 771
- 《水面舰艇编队作战运筹分析》谭安胜著 2009
- 《分析化学》陈怀侠主编 2019
- 《卓有成效的管理者 中英文双语版》(美)彼得·德鲁克许是祥译;那国毅审校 2019
- 《影响葡萄和葡萄酒中酚类特征的因素分析》朱磊 2019
- 《FDS火灾数值模拟》李胜利,李孝斌编著 2019
- 《仪器分析技术 第2版》曹国庆 2018
- 《全国普通高等中医药院校药学类专业十三五规划教材 第二轮规划教材 分析化学实验 第2版》池玉梅 2018
- 《Power BI数据清洗与可视化交互式分析》陈剑 2020
- 《AutoCAD 2018自学视频教程 标准版 中文版》CAD/CAM/CAE技术联盟 2019
- 《行测资料分析》李永新主编 2019
- 《地球简史》(英)戴维·贝克(David Baker) 2020
- 《第三帝国的兴亡》(英)克里斯·毕晓普(Chris Bishop),(英)戴维·乔丹(David Jordan)著 2019
- 《图解轻武器史 剑、矛和锤》(美)大卫·苏德(David Soud)著;刘恒沙译 2017
- 《现代环境主义导论》(英)戴维·佩珀(David Pepper)著 2020
- 《中国经学史》(美)韩大伟(David B. Honey)著 2019
- 《火星生命 前往须知》(美)戴维·温特劳布(DAVID A. WEINTRAUB)著;傅承启译 2019
- 《程序员修炼之道 通向务实的最高境界 第2版》(美)David Thomas(大卫·托马斯),Andrew Hunt(安德鲁·亨特) 2020
- 《谁捉住了上帝粒子?》(法)大卫·卢阿普尔(David Louapre)著 2020
- 《博士生教育的变迁》(澳)大卫·鲍德(David Boud),(澳)艾莉森·李(Alison Lee)编 2019
- 《信息系统安全基础 原书第2版》(美)David Kim 2020
- 《R语言机器学习 原书第2版=MACHINE LEARNING USING R WITH TIME SERIES AND INDUSTRY-BASED USE CASES IN R》SECOND EDITION
- 《机器学习实战 基于SOPHON平台的机器学习理论与实践=MACHINE LEARNING IN ACTION PRINCIPLES AND PRACTICE BASED ON TH》星环科技人工智能平台团队编著 2020
- 《竞争战略 全译珍藏版》(美)迈克尔·波特(Michael E. Porter)著 2012
- 《网络互联技术手册 第2版》(美)(K.唐斯)Kevin Downes等著;包晓露等译 1999
- 《新版交换式以太网和快速型以太网 第2版》(美)(R.布雷耶)Robert Breyer,(美)(S.赖利)Sean Riley著;肖文贵等译 1997
- 《摄影100关键词》(英)克拉克著 2011
- 《数控技术专业英语》高成秀主编 2010
- 《守望百年 中英文对照爱情长诗》蔡丽双著;张智中译 2014
- 《环境政策概要》(英)卡罗琳·斯奈尔(Carolyn Snell)著;宋伟译 2017
- 《驼铃 中-英-波兰文对照诗集》蔡丽双著;张智中,(波兰)博古米娜·雅尼卡译 2015