Handbook for Automatic Computation

Table of Contents

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   Book Overview
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   Chapter 1 Symmetric Decomposition of a Positive Definite Matrix
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   Chapter 2 Iterative Refinement of the Solution of a Positive Definite System of Equations
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   Chapter 3 Inversion of Positive Definite Matrices by the Gauss-Jordan Method
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   Chapter 4 Symmetric Decomposition of Positive Definite Band Matrices
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   Chapter 5 The Conjugate Gradient Method
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   Chapter 6 Solution of Symmetric and Unsymmetric Band Equations and the Calculations of Eigenvectors of Band Matrices
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   Chapter 7 Solution of Real and Complex Systems of Linear Equations
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   Chapter 8 Linear Least Squares Solutions by Housholder Transformations
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    Chapter 9 Elimination with Weighted Row Combinations for Solving Linear Equations and Least Squares Problems
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    Chapter 10 Singular Value Decomposition and Least Squares Solutions
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    Chapter 11 A Realization of the Simplex Method Based on Triangular Decompositions
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    Chapter 12 The Jacobi Method for Real Symmetric Matrices
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    Chapter 13 Householder’s Tridiagonalization of a Symmetric Matrix
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    Chapter 14 The QR and QL Algorithms for Symmetric Matrices
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    Chapter 15 The Implicit QL Algorithm
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    Chapter 16 Calculation of the Eigenvalues of a Symmetric Tridiagonal Matrix by the Method of Bisection
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    Chapter 17 Rational QR Transformation with Newton Shift for Symmetric Tridiagonal Matrices
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    Chapter 18 The Q R Algorithm for Band Symmetric Matrices
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    Chapter 19 Tridiagonalization of a Symmetric Band Matrix
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    Chapter 20 Simultaneous Iteration Method for Symmetric Matrices
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    Chapter 21 Reduction of the Symmetric Eigenproblem Ax = λB x and Related Problems to Standard Form
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    Chapter 22 Balancing a Matrix for Calculation of Eigenvalues and Eigenvectors
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    Chapter 23 Solution to the Eigenproblem by a Norm Reducing Jacobi Type Method
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    Chapter 24 Similarity Reduction of a General Matrix to Hessenberg Form
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    Chapter 25 The QR Algorithm for Real Hessenberg Matrices
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    Chapter 26 Eigenvectors of Real and Complex Matrices by LR and QR triangularizations
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    Chapter 27 The Modified LR Algorithm for Complex Hessenberg Matrices
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    Chapter 28 Solution to the Complex Eigenproblem by a Norm Reducing Jacobi Type Method
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    Chapter 29 The Calculation of Specified Eigenvectors by Inverse Iteration