Saad Study
Reference edition: Yousef Saad, Iterative Methods for Sparse Linear Systems, 2nd ed. (2003).
Source: Author’s public copy · Edition and errata
Study order / Book mapping
| Order | Topic | Book scope |
|---|---|---|
| 00 | Prerequisites | Ch. 1 |
| 01 | Sparse Linear Systems | Ch. 3 |
| 02 | Stationary Iterative Methods | Ch. 4 |
| 03 | Projection Methods | Ch. 5 |
| 04 | Krylov Subspaces | §6.2 |
| 05 | Arnoldi | §§6.3–6.4 |
| 06 | GMRES | §6.5; §6.11.4 |
| 07 | Lanczos | §6.6 |
| 08 | Conjugate Gradient | §6.7; §6.11.3 |
| 09 | Preconditioning | Ch. 9 |
| 10 | Basic Preconditioners | Ch. 10; §12.2 |
| 11 | Nonsymmetric Krylov Methods | Ch. 7; Ch. 8 connection |
| 12 | Convergence and Spectral Interpretation | §6.11; §1.9 |
| 13 | Parallel / PDE Connection | Chs. 2, 11–12 |
| 14 | Domain Decomposition Bridge | Ch. 14; Ch. 13 connection |
Dependency
Linear Algebra prerequisites → Stationary → Projection → Krylov → Arnoldi / Lanczos → GMRES / CG → Preconditioning → Domain Decomposition
Ordering notes
- Review Ch. 1 → Linear Algebra Review
- Revisit the nonsymmetric methods of Ch. 7 in unit 11, after preconditioning in Chs. 9–10, following the requested study sequence.
- Ch. 8 → the normal-equation connection in unit 11.
- Ch. 2 → the PDE connection in unit 13.
- Ch. 12 → block Jacobi in unit 10 and parallel preconditioners in unit 13.
- Ch. 13 → the multigrid connection in unit 14.
- RAS / coarse correction / two-level extensions → headings in unit 14; TODO: verify separate references.
Current next action
- 00. Prerequisites