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Numerical analysis: mathematics of scientific computing Third Edition = 数值分析 (英文版·第3版)PDF|Epub|txt|kindle电子书版本网盘下载
- David Kincaid ; Ward Cheney 著
- 出版社： China Machine Press
- ISBN：7111119134
- 出版时间：2003
- 标注页数：794页
- 文件大小：79MB
- 文件页数：807页
- 主题词：数值计算－高等学校－教材－英文
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图书目录
Numerical Analysis：What Is It？1
1 Mathematical Preliminaries3
1.0 Introduction3
1.1 Basic Concepts and Taylor’s Theorem3
1.2 Orders of Convergence and Additional Basic Concepts15
1.3 Difference Equations28
2 Computer Arithmetic37
2.0 Introduction37
2.1 Floating-Point Numbers and Roundoff Errors37
2.2 Absolute and Relative Errors：Loss of Significance55
2.3 Stable and Unstable Computations：Conditioning64
3 Solution of Nonlinear Equations73
3.0 Introduction73
3.1 Bisection （Interval Halving） Method74
3.2 Newton’s Method81
3.3 Secant Method93
3.4 Fixed Points and Functional Iteration100
3.5 Computing Roots of Polynomials109
3.6 Homotopy and Continuation Methods130
4 Solving Systems of Linear Equations139
4.0 Introduction139
4.1 Matrix Algebra140
4.2 LU and Cholesky Factorizations149
4.3 Pivoting and Constructing an Algorithm163
4.4 Norms and the Analysis of Errors186
4.5 Neumann Series and Iterative Refinement197
4.6 Solution of Equations by Iterative Methods207
4.7 Steepest Descent and Conjugate Gradient Methods232
4.8 Analysis of Roundoff Error in the Gaussian Algorithm245
5 Selected Topics in Numerical Linear Algebra254
5.0 Review of Basic Concepts254
5.1 Matrix Eigenvalue Problem：Power Method257
5.2 Schur’s and Gershgorin’s Theorems265
5.3 Orthogonal Factorizations and Least-Squares Problems273
5.4 Singular-Value Decomposition and Pseudoinverses287
5.5 QR-Algorithm of Francis for the Eigenvalue Problem298
6 Approximating Functions308
6.0 Introduction308
6.1 Polynomial Interpolation308
6.2 Divided Differences327
6.3 Hermite Interpolation338
6.4 Spline Interpolation349
6.5 B-Splines：Basic Theory366
6.6 B-Splines：Applications377
6.7 Taylor Series388
6.8 Best Approximation：Least-Squares Theory392
6.9 Best Approximation：Chebyshev Theory405
6.10 Interpolation in Higher Dimensions420
6.11 Continued Fractions438
6.12 Trigonometric Interpolation445
6.13 Fast Fourier Transform451
6.14 Adaptive Approximation460
7 Numerical Differentiation and Integration465
7.1 Numerical Differentiation and Richardson Extrapolation465
7.2 Numerical Integration Based on Interpolation478
7.3 Gaussian Quadrature492
7.4 Romberg Integration502
7.5 Adaptive Quadrature507
7.6 Sard’s Theory of Approximating Functionals513
7.7 Bernoulli Polynomials and the Euler-Maclaurin Formula519
8 Numerical Solution of Ordinary Differential Equations524
8.0 Introduction524
8.1 The Existence and Uniqueness of Solutions524
8.2 Taylor-Series Method530
8.3 Runge-Kutta Methods539
8.4 Multistep Methods549
8.5 Local and Global Errors：Stability557
8.6 Systems and Higher-Order Ordinary Differential Equations565
8.7 Boundary-Value Problems572
8.8 Boundary-Value Problems：Shooting Methods581
8.9 Boundary-Value Problems：Finite-Differences589
8.10 Boundary-Value Problems：Collocation593
8.11 Linear Differential Equations597
8.12 Stiff Equations608
9 Numerical Solution of Partial Differential Equations615
9.0 Introduction615
9.1 Parabolic Equations：Explicit Methods615
9.2 Parabolic Equations：Implicit Methods623
9.3 Problems Without Time Dependence：Finite-Differences629
9.4 Problems Without Time Dependence：Galerkin Methods634
9.5 First-Order Partial Differential Equations：Characteristics642
9.6 Quasilinear Second-Order Equations：Characteristics650
9.7 Other Methods for Hyperbolic Problems660
9.8 Multigrid Method667
9.9 Fast Methods for Poisson’s Equation676
10 Linear Programming and Related Topics681
10.1 Convexity and Linear Inequalities681
10.2 Linear Inequalities689
10.3 Linear Programming695
10.4 The Simplex Algorithm700
11 Optimization711
11.0 Introduction711
11.1 One-Variable Case712
11.2 Descent Methods716
11.3 Analysis of Quadratic Objective Functions719
11.4 Quadratic-Fitting Algorithms721
11.5 Nelder-Meade Algorithm722
11.6 Simulated Annealing723
11.7 Genetic Algorithms724
11.8 Convex Programming725
11.9 Constrained Minimization726
11.10 Pareto Optimization727
Appendix A An Overview of Mathematical Software731
Bibliography745
Index771