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The Resource Fundamentals of matrix computations, David S. Watkins

Fundamentals of matrix computations, David S. Watkins

Label
Fundamentals of matrix computations
Title
Fundamentals of matrix computations
Statement of responsibility
David S. Watkins
Creator
Subject
Language
eng
http://library.link/vocab/creatorName
Watkins, David S
Illustrations
illustrations
Index
index present
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/subjectName
Matrices
Label
Fundamentals of matrix computations, David S. Watkins
Instantiates
Publication
Bibliography note
Includes bibliographical references and indexes
Contents
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. Gaussian Elimination with 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 Least Squares 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 Revisited -- 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
Control code
ocn500243329
Dimensions
25 cm
Edition
3rd ed
Extent
xvi, 644 p.
Isbn
9780470528334
Isbn Type
(cloth)
Lccn
2010001933
Other physical details
ill.
System control number
(OCoLC)500243329
Label
Fundamentals of matrix computations, David S. Watkins
Publication
Bibliography note
Includes bibliographical references and indexes
Contents
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. Gaussian Elimination with 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 Least Squares 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 Revisited -- 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
Control code
ocn500243329
Dimensions
25 cm
Edition
3rd ed
Extent
xvi, 644 p.
Isbn
9780470528334
Isbn Type
(cloth)
Lccn
2010001933
Other physical details
ill.
System control number
(OCoLC)500243329

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