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Other titles in the Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts series:

Fundamentals of Matrix Computations (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)

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Fundamentals of Matrix Computations (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts) Cover

 

Synopses & Reviews

Publisher Comments:

This new, modernized edition provides a clear and thorough introduction to matrix computations, a key component of scientific computing

Retaining the accessible and hands-on style of its predecessor, Fundamentals of Matrix Computations, Third Edition thoroughly details matrix computations and the accompanying theory alongside the author's useful insights. The book presents the most important algorithms of numerical linear algebra and helps readers to understand how the algorithms are developed and why they work.

Along with new and updated examples, the Third Edition features:

  • A novel approach to Francis' QR algorithm that explains its properties without reference to the basic QR algorithm
  • Application of classical Gram-Schmidt with reorthogonalization
  • A revised approach to the derivation of the Golub-Reinsch SVD algorithm
  • New coverage on solving product eigenvalue problems
  • Expanded treatment of the Jacobi-Davidson method
  • A new discussion on stopping criteria for iterative methods for solving linear equations

Throughout the book, numerous new and updated exercises—ranging from routine computations and verifications to challenging programming and proofs—are provided, allowing readers to immediately engage in applying the presented concepts. The new edition also incorporates MATLAB to solve real-world problems in electrical circuits, mass-spring systems, and simple partial differential equations, and an index of MATLAB terms assists readers with understanding the basic concepts related to the software.

Fundamentals of Matrix Computations, Third Edition is an excellent book for courses on matrix computations and applied numerical linear algebra at the upper-undergraduate and graduate level. The book is also a valuable resource for researchers and practitioners working in the fields of engineering and computer science who need to know how to solve problems involving matrix computations.

Book News Annotation:

This text introduces the fundamentals of numerical linear algebra and matrix computations to advanced undergraduates (and beyond) studying in mathematics, computer science, engineering, and other disciplines where numerical methods are used. Watkins (mathematics, Washington State U.) includes chapters on Gaussian elimination and its variants, sensitivity of linear systems, the least squares problem, the singular value decomposition, eigenvalues and eigenvectors, and iterative methods for linear systems. The material is illustrated using examples and exercises on applications (e.g. electrical circuits, mass-spring systems, and simple partial differential equations) utilizing MATLAB for solutions. For this new edition, he has simplified the presentation of Francis's algorithm (more commonly known as the implicitly shifted QR algorithm) for computing eigenvalues and eigenvectors, among other changes. Prerequisites are a first course in linear algebra and some experience with computer programming. A first course in differential equations may also prove helpful for understanding some of the examples. Annotation ©2010 Book News, Inc., Portland, OR (booknews.com)

Synopsis:

Fundamentals of Matrix Computations, Third Edition thoroughly details matrix computations and the accompanying theory alongside the author's useful insights. Featuring many new and updated examples and exercises that use the MATLAB(R) language, this revision presents the most important algorithms of numerical linear algebra and helps readers to understand how the algorithms are developed and why they work. It also includes modern coverage of Singular Value Decomposition, a streamlined discussion of the Gram-Schmidt process, and a discussion on balancing the eigenvalue problem. Practicing scientists and graduate and advanced undergraduate students will find this popular book more than meets their needs.

About the Author

DAVID S. WATKINS, PhD, is Professor in the Department of Mathematics at Washington State University. He has published more than 100 articles in his areas of research interest, which include numerical linear algebra, numerical analysis, and scientific computing.

Table of Contents

Preface.

Acknowledgments.

1 Gaussian Elimination and Its Variants.

1.1 Matrix Multiplication.

1.2 Systems of Linear Equations.

1.3 Triangular Systems.

1.4 Positive Definite Systems; Cholesky Decomposition.

1.5 Banded Positive Definite Systems.

1.6 Sparse Positive Definite Systems.

1.7 Gaussian Elimination and the LU Decomposition.

1.8 Gaussain Elimination and Pivoting.

1.9 Sparse Gaussian Elimination.

2 Sensitivity of Linear Systems.

2.1 Vector and Matrix Norms.

2.2 Condition Numbers.

2.3 Perturbing the Coefficient Matrix.

2.4 A Posteriori Error Analysis Using the Residual.

2.5 Roundoff Errors; Backward Stability.

2.6 Propagation of Roundoff Errors.

2.7 Backward Error Analysis of Gaussian Elimination.

2.8 Scaling.

2.9 Componentwise Sensitivity Analysis.

3 The Least Squares Problem.

3.1 The Discrete Square Problem.

3.2 Orthogonal Matrices, Rotators and Reflectors.

3.3 Solution of the Least Squares Problem.

3.4 The Gram-Schmidt Process.

3.5 Geometric Approach.

3.6 Updating the QR Decomposition.

4 The Singular Value Decomposition.

4.1 Introduction.

4.2 Some Basic Applications of Singular Values.

4.3 The SVD and the Least Squares Problem.

4.4 Sensitivity of the Least Squares Problem.

5 Eigenvalues and Eigenvectors I.

5.1 Systems of Differential Equations.

5.2 Basic Facts.

5.3 The Power Method and Some Simple Extensions.

5.4 Similarity Transforms.

5.5 Reduction to Hessenberg and Tridiagonal Forms.

5.6 Francis's Algorithm.

5.7 Use of Francis's Algorithm to Calculate Eigenvectors.

5.8 The SVD Revisted.

6 Eigenvalues and Eigenvectors II.

6.1 Eigenspaces and Invariant Subspaces.

6.2 Subspace Iteration and Simultaneous Iteration.

6.3 Krylov Subspaces and Francis's Algorithm.

6.4 Large Sparse Eigenvalue Problems.

6.5 Implicit Restarts.

6.6 The Jacobi-Davidson and Related Algorithms.

7 Eigenvalues and Eigenvectors III.

7.1 Sensitivity of Eigenvalues and Eigenvectors.

7.2 Methods for the Symmetric Eigenvalue Problem.

7.3 Product Eigenvalue Problems.

7.4 The Generalized Eigenvalue Problem.

8 Iterative Methods for Linear Systems.

8.1 A Model Problem.

8.2 The Classical Iterative Methods.

8.3 Convergence of Iterative Methods.

8.4 Descent Methods; Steepest Descent.

8.5 On Stopping Criteria.

8.6 Preconditioners.

8.7 The Conjugate-Gradient Method.

8.8 Derivation of the CG Algorithm.

8.9 Convergence of the CG Algorithm.

8.10 Indefinite and Nonsymmetric Problems.

References.

Index.

Index of MATLAB Terms.

Product Details

ISBN:
9780470528334
Author:
Watkins, David S.
Publisher:
John Wiley & Sons
Subject:
Algebra - Linear
Subject:
Matrices
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
Mathematics-Linear Algebra
Subject:
Linear Algebra
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Subject:
matrix computations, matrix theory, numerical linear algebra algorithms, MATLAB, Fortran, Singular Value Decomposition, Gram-Schmidt process, eigenvalue problem, QR algorithm, Arnoldi process, matrix computations, applied numerical linear algebra, Fortran
Copyright:
Edition Description:
WOL online Book (not BRO)
Series:
Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts
Series Volume:
94
Publication Date:
20100706
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
664
Dimensions:
235 x 164 x 39 mm 36.96 oz

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Fundamentals of Matrix Computations (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts) New Hardcover
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Product details 664 pages John Wiley & Sons - English 9780470528334 Reviews:
"Synopsis" by , Fundamentals of Matrix Computations, Third Edition thoroughly details matrix computations and the accompanying theory alongside the author's useful insights. Featuring many new and updated examples and exercises that use the MATLAB(R) language, this revision presents the most important algorithms of numerical linear algebra and helps readers to understand how the algorithms are developed and why they work. It also includes modern coverage of Singular Value Decomposition, a streamlined discussion of the Gram-Schmidt process, and a discussion on balancing the eigenvalue problem. Practicing scientists and graduate and advanced undergraduate students will find this popular book more than meets their needs.
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