Table of Contents

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.