矩阵迭代分析

出版时间：2006-1  出版社：科学出版社  作者：瓦尔加  页数：372  字数：439000  

内容概要

《矩阵迭代分析(第二版)》的作者现任英国肯特大学教授，多种国际权威杂志主编或编委。本书第一版1962年由Prentice Hall出版，是矩阵迭代分析方面的经典教材。此次修订，有些章节吸收了新的研究成果，如弱正则分裂方面的结果；有些章节则增添了新的内容，引述了最近的定理，更新了参考文献，读者从中可以了解一些最新的发展方向。此次修订，新的章节的内容基本上都是自含的，并添加了习题。原版主要基于线性代数方法，而修订版强调借助其他领域的工具，如逼近论和共型映射理论，得到更加新颖的结果。本书尤其适合从事数值分析的科研人员和研究生阅读。

书籍目录

1. Matrix Properties and Concepts  1.1 Introduction  1.2 A Simple Example  1.3 Norms and Spectral Radii  1.4 Bounds for the Spectral Radius of a Matrix and Directed Graphs  1.5 Diagonally Dominant Matrices  1.6 Ovals of Cassini2. Nonnegative Matrices  2.1 Spectral Radii of Nonnegative Matrices  2.2 Cyclic and Primitive Matrices  2.3 Reducible Matrices  2.4 Nonnegative Matrices and Directed Graphs3. Basic Iterative Methods and Comparison Theorems  3.1 The Point Jacobi, Gauss-Seidel, and Successive Overrelaxation Iterative Methods  3.2 Average Rates of Convergence  3.3 The Stein-Rosenberg Theorem  3.4 The Ostrowski-Reich Theorem  3.5 Stieltjes Matrices, M-Matrices and H-Matrices  3.6 Regular and Weak Regular Splittings of Matrices4. Successive Overrelaxation Iterative Methods  4.1 p-Cyclic Matrices  4.2 The Successive Overrelaxation Iterative Method for p-Cyclic Matrices  4.3 Theoretical Determination of an Optimum Relaxation Factor  4.4 Extensions of the 2-Cyclic Theory of Matrices  4.5 Asymptotic Rates of Convergence  4.6 CO(q,r) and GCO(q,r): Generalized Consistent Orderings5. Semi-Iterative Methods  5.1 Semi-Iterative Methods and Chebyshev Polynomials  5.2 Relationship of Semi-Iterative Methods to Successive Overrelaxation Iterative Methods  5.3 Comparison of Average Rates of Convergence: the Weakly Cyclic Case  5.4 Cyclic Reduction and Related Iterative Methods  5.5 Semi-Iterative Methods Applied to the Successive Overrelaxation Method6. Derivation and Solution of Elliptic Difference Equations  6.1 A Simple Two-Point boundary-Value Problem  6.2 General Second-Order Ordinary Differential Equations  6.3 Derivation of Finite Difference Approximations in Higher Dimensions  6.4 Factorization Techniques and block Iterative Methods  6.5 Asymptotic Convergence Rates for the Model Problem7. Alternating-Direction Implicit Iterative Methods  7.1 The Peaceman-Rachford Iterative Method  7.2 The Commutative Case  7.3 The Noncommutative Case  7.4 Variants of the Peaceman-Rachford Iterative Method8. Matrix Methods for Parabolic Partial Differential Equations  8.1 Semi-Discrete Approximation  8.2 Essentially Positive Matrices  8.3 Matrix Approximations for exp (-tS)  8.4 Relationship with Iterative Metholds for Solving Elliptic Difference Equations  8.5 Chebyshev Rational Approximations for exp (-tS)9. Estimation of Acceleration Parameters  9.1 Application of the Theory of Nonnegative Matrices  9.2 Application of Isoperimetric InequalitiesA. AppendixB. AppendixReferencesIndex

用户评论 (总计10条)

•   这本书在矩阵迭代领域,属于最经典的一本.瓦格先生的个人网站上面,有几乎所有他发表的文章,建议大家去看一下.
•   国外经典数学名著，内容全面，数值代数方面的工具书
•   这本书应该是非常经典的一本书。1966年有蒋尔雄等三位先生经典的翻译，62年第一版，99年第二版，呵呵，瓦格先生真是非常有耐心啊，不象国内某些书一年都有好几版的，真心难得。值得推荐！
•   Varga的文章在个人主页上有，我们直接可以下到。挺好的，如果相爱那个进一步了解的话，可以去看看。
•   还没看，不过应该不错，老师推荐的
•   还没看，看评论不错
•   绝版之前终于买到了
•   可以和张贤达的《矩阵分析与应用》一并使用
•   好书要慢慢看,虽然没看完,但是觉得不错,推荐中
•   买来储备着