Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Direct Solution Methods
- 2 Theory of Matrix Eigenvalues
- 3 Positive Definite Matrices, Schur Complements, and Generalized Eigenvalue Problems
- 4 Reducible and Irreducible Matrices and the Perron-Frobenius Theory for Nonnegative Matrices
- 5 Basic Iterative Methods and Their Rates of Convergence
- 6 M-Matrices, Convergent Splittings, and the SOR Method
- 7 Incomplete Factorization Preconditioning Methods
- 8 Approximate Matrix Inverses and Corresponding Preconditioning Methods
- 9 Block Diagonal and Schur Complement Preconditionings
- 10 Estimates of Eigenvalues and Condition Numbers for Preconditioned Matrices
- 11 Conjugate Gradient and Lanczos-Type Methods
- 12 Generalized Conjugate Gradient Methods
- 13 The Rate of Convergence of the Conjugate Gradient Method
- Appendices
- Index
10 - Estimates of Eigenvalues and Condition Numbers for Preconditioned Matrices
Published online by Cambridge University Press: 05 August 2012
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Direct Solution Methods
- 2 Theory of Matrix Eigenvalues
- 3 Positive Definite Matrices, Schur Complements, and Generalized Eigenvalue Problems
- 4 Reducible and Irreducible Matrices and the Perron-Frobenius Theory for Nonnegative Matrices
- 5 Basic Iterative Methods and Their Rates of Convergence
- 6 M-Matrices, Convergent Splittings, and the SOR Method
- 7 Incomplete Factorization Preconditioning Methods
- 8 Approximate Matrix Inverses and Corresponding Preconditioning Methods
- 9 Block Diagonal and Schur Complement Preconditionings
- 10 Estimates of Eigenvalues and Condition Numbers for Preconditioned Matrices
- 11 Conjugate Gradient and Lanczos-Type Methods
- 12 Generalized Conjugate Gradient Methods
- 13 The Rate of Convergence of the Conjugate Gradient Method
- Appendices
- Index
Summary
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- Iterative Solution Methods , pp. 402 - 448Publisher: Cambridge University PressPrint publication year: 1994