The Lanczos and conjugate gradient algorithms : from theory to finite precision computations

Preface 1. The Lanczos algorithm in exact arithmetic 2. The CG algorithm in exact arithmetic 3. A historical perspective on the Lanczos algorithm in finite precision 4. The Lanczos algorithm in finite precision 5. The CG algorithm in finite precision 6. The maximum attainable accuracy 7. Estimates of norms of the error in finite precision 8. The preconditioned CG algorithm 9. Miscellaneous Appendix Bibliography Index.