应用数值线性代数 英文影印版pdf电子书版本下载

点此进入-本书在线PDF格式电子书下载【推荐-云解压-方便快捷】直接下载PDF格式图书。移动端-PC端通用
种子下载[BT下载速度快] 温馨提示：（请使用BT下载软件FDM进行下载）软件下载地址页 直链下载[便捷但速度慢]   [在线试读本书]   [在线获取解压码]

应用数值线性代数 英文影印版PDF格式电子书版下载

下载的文件为RAR压缩包。需要使用解压软件进行解压得到PDF格式图书。

建议使用BT下载工具Free Download Manager进行下载,简称FDM(免费,没有广告,支持多平台）。本站资源全部打包为BT种子。所以需要使用专业的BT下载软件进行下载。如 BitComet qBittorrent uTorrent等BT下载工具。迅雷目前由于本站不是热门资源。不推荐使用！后期资源热门了。安装了迅雷也可以迅雷进行下载！

（文件页数 要大于 标注页数，上中下等多册电子书除外）

注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具

1 Introduction 1

1.1 Basic Notation 1

1.2 Standard Problems of Numerical Linear Algebra 1

1.3 General Techniques 2

1.3.1 Matrix Factorizations 3

1.3.2 Perturbation Theory and Condition Numbers 4

1.3.3 Effects of Roundoff Error on Algorithms 5

1.3.4 Analyzing the Speed of Algorithms 5

1.3.5 Engineering Numerical Software 6

1.4 Example:Polynomial Evaluation 7

1.5 Floating Point Arithmetic 9

1.5.1 Further Details 12

1.6 Polynomial Evaluation Revisited 15

1.7 Vector and Matrix Norms 19

1.8 References and Other Topics for Chapter 1 23

1.9 Questions for Chapter 1 24

2 Linear Equation Solving 31

2.1 Introduction 31

2.2 Perturbation Theory 32

2.2.1 Relative Perturbation Theory 35

2.3 Gaussian Elimination 38

2.4 Error Analysis 44

2.4.1 The Need for Pivoting 45

2.4.2 Formal Error Analysis of Gaussian Elimination 46

2.4.3 Estimating Condition Numbers 50

2.4.4 Practical Error Bounds 54

2.5 Improving the Accuracy of a Solution 60

2.5.1 Single Precision Iterative Refinement 62

2.5.2 Equilibration 62

2.6 Blocking Algorithms for Higher Performance 63

2.6.1 Basic Linear Algebra Subroutines(BLAS) 66

2.6.2 How to Optimize Matrix Multiplication 67

2.6.3 Reorganizing Gaussian Elimination to Use Level 3 BLAS 72

2.6.4 More About Parallelism and Other Performance Issues 75

2.7 Special Linear Systems 76

2.7.1 Real Symmetric Positive Definite Matrices 76

2.7.2 Symmetric Indefinite Matrices 79

2.7.3 Band Matrices 79

2.7.4 General Sparse Matrices 83

2.7.5 Dense Matrices Depending on Fewer Than O(n2)Pa-rameters 90

2.8 References and Other Topics for Chapter 2 93

2.9 Questions for Chapter 2 93

3 Linear Least Squares Problems 101

3.1 Introduction 101

3.2 Matrix Factorizations That Solve the Linear Least Squares Prob-lem 105

3.2.1 Normal Equations 106

3.2.2 QR Decomposition 107

3.2.3 Singular Value Decomposition 109

3.3 Perturbation Theory for the Least Squares Problem 117

3.4 Orthogonal Matrices 118

3.4.1 Householder Transformations 119

3.4.2 Givens Rotations 121

3.4.3 Roundoff Error Analysis for Orthogonal Matrices 123

3.4.4 Why Orthogonal Matrices? 124

3.5 Rank-Deficient Least Squares Problems 125

3.5.1 Solving Rank-Deficient Least Squares Problems Using the SVD 128

3.5.2 Solving Rank-Deficient Least Squares Problems Using QR with Pivoting 130

3.6 Performance Comparison of Methods for Solving Least Squares Problems 132

3.7 References and Other Topics for Chapter 3 134

3.8 Questions for Chapter 3 134

4 Nonsymmetric Eigenvalue Problems 139

4.1 Introduction 139

4.2 Canonical Forms 140

4.2.1 Computing Eigenvectors from the Schur Form 148

4.3 Perturbation Theory 148

4.4 Algorithms for the Nonsymmetric Eigenproblem 153

4.4.1 Power Method 154

4.4.2 Inverse Iteration 155

4.4.3 Orthogonal Iteration 156

4.4.4 QR Iteration 159

4.4.5 Making QR Iteration Practical 163

4.4.6 Hessenberg Reduction 164

4.4.7 Tridiagonal and Bidiagonal Reduction 166

4.4.8 QR Iteration with Implicit Shifts 167

4.5 Other Nonsymmetric Eigenvalue Problems 173

4.5.1 Regular Matrix Pencils and Weierstrass Canonical Form 173

4.5.2 Singular Matrix Pencils and the Kronecker Canonical Form 180

4.5.3 Nonlinear Eigenvalue Problems 183

4.6 Summary 184

4.7 References and Other Topics for Chapter 4 187

4.8 Questions for Chapter 4 187

5 The Symmetric Eigenproblem and Singular Value Decompo-sition 195

5.1 Introduction 195

5.2 Perturbation Theory 197

5.2.1 Relative Perturbation Theory 207

5.3 Algorithms for the Symmetric Eigenproblem 210

5.3.1 Tridiagonal QR Iteration 212

5.3.2 Rayleigh Quotient Iteration 214

5.3.3 Divide-and-Conquer 216

5.3.4 Bisection and Inverse Iteration 228

5.3.5 Jacobi's Method 232

5.3.6 Performance Comparison 235

5.4 Algorithms for the Singular Value Decomposition 237

5.4.1 QR Iteration and Its Variations for the Bidiagonal SVD 242

5.4.2 Computing the Bidiagonal SVD to High Relative Accuracy 245

5.4.3 Jacobi's Method for the SVD 248

5.5 Differential Equations and Eigenvalue Problems 254

5.5.1 The Toda Lattice 255

5.5.2 The Connection to Partial Differential Equations 259

5.6 References and Other Topics for Chapter 5 260

5.7 Questions for Chapter 5 260

6 Iterative Methods for Linear Systems 265

6.1 Introduction 265

6.2 On-line Help for Iterative Methods 266

6.3 Poisson's Equation 267

6.3.1 Poisson's Equation in One Dimension 267

6.3.2 Poisson's Equation in Two Dimensions 270

6.3.3 Expressing Poisson's Equation with Kronecker Products 274

6.4 Summary of Methods for Solving Poisson's Equation 277

6.5 Basic Iterative Methods 279

6.5.1 Jacobi's Method 281

6.5.2 Gauss-Seidel Method 282

6.5.3 Successive Overrelaxation 283

6.5.4 Convergence of Jacobi's,Gauss-Seidel,and SOR(ω) Methods on the Model Problem 285

6.5.5 Detailed Convergence Criteria for Jacobi's,Gauss-Seidel,and SOR(ω)Methods 286

6.5.6 Chebyshev Acceleration and Symmetric SOR(SSOR) 294

6.6 Krylov Subspace Methods 299

6.6.1 Extracting Information about A via Matrix-Vector Mul-tiplication 301

6.6.2 Solving Ax=b Using the Krylov Subspace κk 305

6.6.3 Conjugate Gradient Method 307

6.6.4 Convergence Analysis of the Conjugate Gradient Method 312

6.6.5 Preconditioning 316

6.6.6 Other Krylov Subspace Algorithms for Solving Ax=b 319

6.7 Fast Fourier Transform 321

6.7.1 The Discrete Fourier Transform 323

6.7.2 Solving the Continuous Model Problem Using Fourier Series 324

6.7.3 Convolutions 325

6.7.4 Computing the Fast Fourier Transform 326

6.8 Block Cyclic Reduction 327

6.9 Multigrid 331

6.9.1 Overview of Multigrid on the Two-Dimensional Poisson's Equation 332

6.9.2 Detailed Description of Multigrid on the One-Dimensional Poisson's Equation 337

6.10 Domain Decomposition 347

6.10.1 Nonoverlapping Methods 348

6.10.2 Overlapping Methods 351

6.11 References and Other Topics for Chapter 6 356

6.12 Questions for Chapter 6 356

7 Iterative Methods for Eigenvalue Problems 361

7.1 Introduction 361

7.2 The Rayleigh-Ritz Method 362

7.3 The Lanczos Algorithm in Exact Arithmetic 366

7.4 The Lanczos Algorithm in Floating Point Arithmetic 375

7.5 The Lanczos Algorithm with Selective Orthogonalization 382

7.6 Beyond Selective Orthogonalization 383

7.7 Iterative Algorithms for the Nonsymmetric Eigenproblem 384

7.8 References and Other Topics for Chapter 7 386

7.9 Questions for Chapter 7 386

Bibliography 389

Index 409