Krylov Solvers for Linear Algebraic Systems: Krylov Solvers

Contents 1. Introduction. 2. The long recurrences. 3. The short recurrences. 4. The Krylov aspects. 5. Transpose-free methods. 6. More on QMR. 7. Look-ahead methods. 8. General block methods. 10. And in practice? 11. Preconditioning. 12. Duality. Appendices. A. Reduction of upper Hessenberg matrix to upper triangular form by plane rotations. B. Schur complements. C. The Jordan form. D. Chebychev polynomials. E. The companion matrix. F. Algorithmic details.