矩陣計算（英文版·第3版）

內容簡介

本書是數值計算領域的名著，系統介紹了矩陣計算的基本理論和方法。內容包括：矩陣乘法、矩陣淚促仔趨分析、線性方程組、正交化和最小二乘法、特徵值問題、Lanczos方法、矩陣函式及鞏旬厚專題討論等。書中的許多算法都有現成的軟體包實現，每節後還附有習題，並有注釋和大量參考文獻。

本書可作為高等催備企少學校數學系高年級本科生和研究生的教材，煮戒察亦可作為計算數學己遷汽良辯寒和工程技術人員的參煉全考用書。

圖書目錄

1Matrix Multiplication Problems1

1.1Basic Algorithms and Notation2

1.2Exploiting Structure 16

1.3Block Matrices and Algorithms24

1.4Vectorization and Re-Use Issues34

2Matrix Analysis48

2.1Basic Ideas from Linear Algebra48

2.2Vector Norms 52

2.3Matrix Norms 54

2.4Finite Precision Matrix Computations59

2.5Orthogonality and the SVD69

2.6Projections and the CS Decomposition75

2.7The Sensitivity of Square Linear Systems80

3General Linear Systems87

3.1Triangular Systems88

3.2The LU Factorization94

3.3Roundoff Analysis of Gaussian Elimination104

3.4Pivoting109

3.5Improving and Estimating Accuracy123

4Special Linear Systems

4.1The LDMT and LDLT Factorizations135

4.2Positive Definite Systems140

4.3Banded Systems152

4.4Symmetric Indefinite Systems161

4.5Block Systems174

4.6Vandermonde Systems and the FFT183

4.7Toeplitz and Related Systems193

5Orthogonalization and Least Squares206

5.1Householder and Givens Matrices208

5.2The QR Factorization223

5.3The Full Rank LS Problem236

5.4Other Orthogonal Factorizations248

5.5The Rank Deficient LS Problem256

5.6Weighting and Iterative Improvement264

5.7Square and Underdetermined Systems270

6Parallel Matrix Computations275

6.1Basic Concepts276

6.2Matrix Multiplication292

6.3Factorizations300

7The Unsymmetric Eigenvalue Problem308

7.1Properties and Decompositions310

7.2Perturbation Theory320

7.3Power Iterations330

7.4The Hessenberg and Real Schur Forms341

7.5The Practical QR Algorithm352

7.6Invariant Subspace Computations362

7.7The QZ Method for Ax=A Bx375

8The Symmetric Eigenvalue Problem391

8.1Properties and Decompositions393

8.2Power Iterations405

8.3The Symmetric QR Algorithm414

8.4Jacobi Methods426

8.5Tridiagonal Methods439

8.6Computing the SVD448

8.7Some Generalized Eigenvalue Problems461

9Lanczos Methods470

9.1Derivation and Convergence Properties471

9.2Practical Lanczos Procedures479

9.3Applications to Ax=b and Least Squares490

9.4Arnoldi and Unsymmetric Lanczos499

10Iterative Methods for Linear Systems508

10.1The Standard Iterations509

10.2The Conjugate Gradient Method520

10.3Preconditioned Conjugate Gradients532

10.4Other Krylov Subspace Methods544

11Functions of Matrices555

11.1Eigenvalue Methods556

11.2Approximation Methods562

11.3The Matrix Exponential572

12Special Topics579

12.1Constrained Least Squares580

12.2Subset Selection Using the SVD590

12.3Total Least Squares595

12.4Computing Subspaces with the SVD601

12.5Updating Matrix Factorizations606

12.6Modified/Structured Eigenproblems621

Index637

矩陣計算（英文版·第3版）

基本介紹

內容簡介

圖書目錄

相關詞條

熱門詞條