Iterative Solution of Large Sparse Systems of Equations - Info and Reading Options

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Intro -- Preface -- Contents -- List of Symbols and Abbreviations -- Symbols -- Greek Letters -- Latin Letters -- Abbreviations and Algorithms -- Part I Linear Iterations -- 1 Introduction -- 1.1 Historical Remarks Concerning Iterative Methods -- 1.2 Model Problem: Poisson Equation -- 1.3 Notation -- 1.3.1 Index Sets, Vectors, and Matrices -- 1.3.2 Star Notation -- 1.4 A Single System Versus a Family of Systems -- 1.5 Amount of Work for the Direct Solution of a Linear System -- 1.6 Examples of Iterative Methods -- 1.7 Sparse Matrices Versus Fully Populated Matrices -- 2 Iterative Methods -- 2.1 Consistency and Convergence -- 2.1.1 Notation -- 2.1.2 Fixed Points -- 2.1.3 Consistency -- 2.1.4 Convergence -- 2.1.5 Convergence and Consistency -- 2.1.6 Defect Correction as an Example of an Inconsistent Iteration -- 2.2 Linear Iterative Methods -- 2.2.1 Notation, First Normal Form -- 2.2.2 Consistency and Second Normal Form -- 2.2.3 Third Normal Form -- 2.2.4 Representation of the Iterates xm -- 2.2.5 Convergence -- 2.2.6 Convergence Speed -- 2.2.7 Remarks Concerning the Matrices M, N, and W -- 2.2.8 Three-Term Recursions, Two- and Multi-Step Iterations -- 2.3 Efficacy of Iterative Methods -- 2.3.1 Amount of Computational Work -- 2.3.2 Efficacy -- 2.3.3 Order of Linear Convergence -- 2.4 Test of Iterative Methods -- 2.4.1 Consistency Test -- 2.4.2 Convergence Test -- 2.4.3 Test by the Model Problem -- 2.4.4 Stopping Criterion -- 3 Classical Linear Iterations in the Positive Definite Case -- 3.1 Eigenvalue Analysis of the Model Problem -- 3.2 Traditional Linear Iterations -- 3.2.1 Richardson Iteration -- 3.2.2 Jacobi Iteration -- 3.2.3 Gauss-Seidel Iteration -- 3.2.4 SOR Iteration -- 3.3 Block Versions -- 3.3.1 Block Structure -- 3.3.2 Block-Jacobi Iteration -- 3.3.3 Block-Gauss-Seidel Iteration -- 3.3.4 Block-SOR Iteration

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