发表于2024-11-21
圖靈原版數學·統計學係列:矩陣計算(英文版·第4版) pdf epub mobi txt 電子書 下載 2024
國際上關於數值綫性代數方麵,全麵的一本專著。
《圖靈原版數學·統計學係列:矩陣計算(英文版·第4版)》是數值計算領域的名著,係統介紹瞭矩陣計算的基本理論和方法。內容包括:矩陣乘法、矩陣分析、綫性方程組、正交化和小二乘法、特徵值問題、Lanczos 方法、矩陣函數及專題討論等。書中的許多算法都有現成的軟件包實現,每節後附有習題,並有注釋和大量參考文獻。新版增加約四分之一內容,反映瞭近年來矩陣計算領域的飛速發展。
《圖靈原版數學·統計學係列:矩陣計算(英文版·第4版)》可作為高等院校數學係高年級本科生和研究生教材,亦可作為計算數學和工程技術人員參考書。
Gene H. Golub(1932-2007), 美國科學院、工程院和藝術科學院院士,世界著名數值分析專傢,現代矩陣計算奠基人,矩陣分解算法的主要貢獻者。生前曾任斯坦福大學教授。
Charles F. Van Loan,著名數值分析專傢,美國康奈爾大學教授,曾任該校計算機科學係主任。他於1973年在密歇根大學獲得博士學位,師從Cleve Moler。
★“多年來,這本書一直是我在研究生院講授‘數值綫性代數’的教材。”
——袁亞湘,中科院院士,中國運籌學學會理事長,馮康奬得主
★“本書內容非常豐富,有老而經典的,也有新的正在研究中的課題。無論你是數值綫性代數領域的工作人員,還是學生,這都是一本有價值的參考書。”
——SIAM Review
1 Matrix Multiplication
1.1 Basic Algorithms and Notation
1.2 Structure and Efficiency
1.3 Block Matrices and Algorithms
1.4 Fast Matrix-Vector Products
1.5 Vectorization and Locality
1.6 Parallel Matrix Multiplication
2 Matrix Analysis
2.1 Basic Ideas from Linear Algebra
2.2 Vector Norms
2.3 Matrix Norms
2.4 The Singular Value Decomposition
2.5 Subspace Metrics
2.6 The Sensitivity of Square Systems
2.7 Finite Precision Matrix Computations
3 General Linear Systems
3.1 Triangular Systems
3.2 The LU Factorization
3.3 Roundoff Error in Gaussian Elimination
3.4 Pivoting
3.5 Improving and Estimating Accuracy
3.6 Parallel LU
4 Special Linear Systems
4.1 Diagonal Dominance and Symmetry
4.2 Positive Definite Systems
4.3 Banded Systems
4.4 Symmetric Indefinite Systems
4.5 Block Tridiagonal Systems
4.6 Vandermonde Systems
4.7 Classical Methods for Toeplitz Systems
4.8 Circulant and Discrete Poisson Systems
5 Orthogonalization and Least Squares
5.1 Householder and Givens Transformations
5.2 The QR Factorization
5.3 The Full-Rank Least Squares Problem
5.4 Other Orthogonal Factorizations
5.5 The Rank-Deficient Least Squares Problem
5.6 Square and Underdetermined Systems
6 Modified Least Squares Problems and Methods
6.1 Weighting and Regularization
6.2 Constrained Least Squares
6.3 Total Least Squares
6.4 Subspace Computations with the SVD
6.5 Updating Matrix Factorizations
7 Unsymmetric Eigenvalue Problems
7.1 Properties and Decompositions
7.2 Perturbation Theory
7.3 Power Iterations
7.4 The Hessenberg and Real Schur Forms
7.5 The Practical QR Algorithm
7.6 Invariant Subspace Computations
7.7 The Generalized Eigenvalue Problem
7.8 Hamiltonian and Product Eigenvalue Problems
7.9 Pseudospectra
8 Symmetric Eigenvalue Problems
8.1 Properties and Decompositions
8.2 Power Iterations
8.3 The Symmetric QR Algorithm
8.4 More Methods for Tridiagonal Problems
8.5 Jacobi Methods
8.6 Computing the SVD
8.7 Generalized Eigenvalue Problems with Symmetry
9 Functions of Matrices
9.1 Eigenvalue Methods
9.2 Approximation Methods
9.3 The Matrix Exponential
9.4 The Sign, Square Root, and Log of a Matrix
10 Large Sparse Eigenvalue Problems
10.1 The Symmetric Lanczos Process
10.2 Lanczos, Quadrature, and Approximation
10.3 Practical Lanczos Procedures
10.4 Large Sparse SVD Frameworks
10.5 Krylov Methods for Unsymmetric Problems
10.6 Jacobi-Davidson and Related Methods
11 Large Sparse Linear System Problems
11.1 Direct Methods
11.2 The Classical Iterations
11.3 The Conjugate Gradient Method
11.4 Other Krylov Methods
11.5 Preconditioning
11.6 The Multigrid Framework
12 Special Topics
12.1 Linear Systems with Displacement Structure
12.2 Structured-Rank Problems
12.3 Kronecker Product Computations
12.4 Tensor Unfoldings and Contractions
12.5 Tensor Decompositions and Iterations
Index
原版書英文質量好~~~~~~~~~~~
評分好好好好好好好好好好好好書
評分不錯
評分雖然有清晰電子版,還是紙質書舒服
評分一般,內容全麵。做參考書!
評分很詳細,不錯的工具書
評分計算數學,矩陣計算的經典之作,羅列很多矩陣算法,具有很好的參考性。
評分 評分不錯
圖靈原版數學·統計學係列:矩陣計算(英文版·第4版) pdf epub mobi txt 電子書 下載