矩陣迭代分析

內(nèi)容概要

《矩陣迭代分析(第二版)》的作者現(xiàn)任英國肯特大學教授，多種國際權威雜志主編或編委。本書第一版1962年由Prentice Hall出版，是矩陣迭代分析方面的經(jīng)典教材。此次修訂，有些章節(jié)吸收了新的研究成果，如弱正則分裂方面的結果；有些章節(jié)則增添了新的內(nèi)容，引述了最近的定理，更新了參考文獻，讀者從中可以了解一些最新的發(fā)展方向。此次修訂，新的章節(jié)的內(nèi)容基本上都是自含的，并添加了習題。原版主要基于線性代數(shù)方法，而修訂版強調(diào)借助其他領域的工具，如逼近論和共型映射理論，得到更加新穎的結果。本書尤其適合從事數(shù)值分析的科研人員和研究生閱讀。

書籍目錄

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

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