'… likely to be an important reference for theoreticians interested in the development and analysis of iterative solution methods for years to come.' Bulletin of the Institute of Mathematics and its Applications

• 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.

'… likely to be an important reference for theoreticians interested in the development and analysis of iterative solution methods for years to come.' Bulletin of the Institute of Mathematics and its Applications

• 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.

'… likely to be an important reference for theoreticians interested in the development and analysis of iterative solution methods for years to come.' Bulletin of the Institute of Mathematics and its Applications

• 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.