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The Theory of Matrices in Numerical Analysis Paperback – Jan 20 2006

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Product Details

  • Paperback: 270 pages
  • Publisher: Dover Publications (Jan. 20 2006)
  • Language: English
  • ISBN-10: 0486449726
  • ISBN-13: 978-0486449722
  • Product Dimensions: 13.7 x 1.5 x 20.7 cm
  • Shipping Weight: 299 g
  • Average Customer Review: 5.0 out of 5 stars 1 customer review
  • Amazon Bestsellers Rank: #2,379,233 in Books (See Top 100 in Books)
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Format: Paperback
Originally published in 1964 and first published by Dover in 1975, the content in this book is a flashback to the days before technology simplified matrix operations. All of the processes are expressed in the form of mathematical theory, there are very few, if any, worked examples. Problems and exercises appear at the end of each chapter but they also deal with theory rather than specific problems to solve. No solutions are given.
The chapter headings are:

*) Some basic identities and inequalities
*) Norms, bounds and convergence
*) Localization theorems and other inequalities
*) The solution of linear systems: methods of successive approximations
*) Direct methods of inversion
*) Proper values and vectors: normalization and reduction of the matrix
*) Proper values and vectors: successive approximations

The word “theory” is correctly used in the title, this book is about how things work, not how they are used in practice.
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Amazon.com: HASH(0xa5a0ad50) out of 5 stars 1 review
8 of 12 people found the following review helpful
HASH(0xa4be7c24) out of 5 stars A classic June 5 2008
By Uttar - Published on Amazon.com
Format: Paperback
Table of contents

1. SOME BASIC IDENTITIES AND INEQUALITIES
1.0 Objectives; Notation
1.1 Elementary Matrices
1.2 Some Factorizations
1.3 Projections, and the General Reciprocal
1.4 Some Determinantal Identities
1.5 Lanczos Algorithm for Tridiagonalization
1.6 Orthogonal Polynomials
References
Problems and Exercises

2. NORMS, BOUNDS, AND CONVERGENCE
2.0 The Notion of a Norm
2.1 Convex Sets and Convex Bodies
2.2 Norms and Bounds
2.3 Norms, Bounds, and Spectral Radii
2.4 Nonnegative Matrices
2.5 Convergence; Functions of Matrices
References
Problems and Exercises

3. LOCALIZATION THEOREMS AND OTHER INEQUALITIES
3.0 Basic Definitions
3.1 Exclusion Theorems
3.2 Inclusion and Separation Theorems
3.3 Minimax Theorems and the Field of Values
3.4 Inequalities of Wielandt Kantorovich
References
Problems and Exercises

4. THE SOLUTION OF LINEAR SYSTEMS: METHODS OF SUCCESSIVE APPROXIMATION
4.0 Direct Methods and Others
4.1 The Inversion of Matrices
4.2 Methods of Projection
4.3 Norm-Reducing Methods
References
Problems and Exercises

5. DIRECT METHODS OF INVERSION
5.0 Uses of the Inverse
5.1 The Method of Modification
5.2 Triangularization
5.3 A More General Formulation
5.4 Orthogonal Triangularization
5.5 Orthogonalization
5.6 Orthogonalization and Projection
5.7 The Method of Conjugate Gradients
References
Problems and Exercises

6. PROPER VALUES AND VECTORS: NORMALIZATION AND REDUCTION OF THE MATRIX
6.0 Purpose of Normalization
6.1 The Method of Krylov
6.2 The Weber-Voetter Method
6.3 The Method of Danilevskii
6.4 The Hessenberg and the Lanczos Reductions
6.5 Proper Values and Vectors
6.6 The Method of Samuelson and Bryan
6.7 The Method of Leverrier
References
Problems and Exercises

7. PROPER VALUES AND VECTORS: SUCCESSIVE APPROXIMATION
7.0 Methods of Successive Approximation
7.1 The Method of Jacobi
7.2 The Method of Collar and Jahn
7.3 Powers of a Matrix
7.4 Simple Iteration (the Power Method)
7.5 Multiple Roots and Principal Vectors
7.6 Staircase Iteration (Treppeniteration)
7.7 The LR-Transformation
7.8 Bi-iteration
7.9 The QR-Transformation
References
Problems and Exercises

BIBLIOGRAPHY
INDEX


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