The Theory of Matrices in Numerical Analysis

Nonfiction, Science & Nature, Mathematics, Matrices
Cover of the book The Theory of Matrices in Numerical Analysis by Alston S. Householder, Dover Publications
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Author: Alston S. Householder ISBN: 9780486145631
Publisher: Dover Publications Publication: June 18, 2013
Imprint: Dover Publications Language: English
Author: Alston S. Householder
ISBN: 9780486145631
Publisher: Dover Publications
Publication: June 18, 2013
Imprint: Dover Publications
Language: English
This text explores aspects of matrix theory that are most useful in developing and appraising computational methods for solving systems of linear equations and for finding characteristic roots. Suitable for advanced undergraduates and graduate students, it assumes an understanding of the general principles of matrix algebra, including the Cayley-Hamilton theorem, characteristic roots and vectors, and linear dependence.
An introductory chapter covers the Lanczos algorithm, orthogonal polynomials, and determinantal identities. Succeeding chapters examine norms, bounds, and convergence; localization theorems and other inequalities; and methods of solving systems of linear equations. The final chapters illustrate the mathematical principles underlying linear equations and their interrelationships. Topics include methods of successive approximation, direct methods of inversion, normalization and reduction of the matrix, and proper values and vectors. Each chapter concludes with a helpful set of references and problems.
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This text explores aspects of matrix theory that are most useful in developing and appraising computational methods for solving systems of linear equations and for finding characteristic roots. Suitable for advanced undergraduates and graduate students, it assumes an understanding of the general principles of matrix algebra, including the Cayley-Hamilton theorem, characteristic roots and vectors, and linear dependence.
An introductory chapter covers the Lanczos algorithm, orthogonal polynomials, and determinantal identities. Succeeding chapters examine norms, bounds, and convergence; localization theorems and other inequalities; and methods of solving systems of linear equations. The final chapters illustrate the mathematical principles underlying linear equations and their interrelationships. Topics include methods of successive approximation, direct methods of inversion, normalization and reduction of the matrix, and proper values and vectors. Each chapter concludes with a helpful set of references and problems.

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