Iterative Solution Methods

This is a useful resource book for students, tutors and researchers using iterative methods.

Zusammenfassung
This book deals primarily with the numerical solution of linear systems of equations by iterative methods. A valuable resource for students and researchers alike wishing to learn more about iterative methods.

Inhalt
Preface; Acknowledgements; 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 preconditional matrices; 11. Conjugate gradient and Lanczos-type methods; 12. Generalized conjugate gradient methods; 13. The rate of convergence of the conjugate gradient method; Appendices.

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