Lecture Notes:

  1. Introduction (13 MB)
  2. Fixed-Point Iterations, Krylov Spaces, and Krylov Methods
  3. Comparing CG and GMRES for Various Model Problems
  4. Convergence of CG – part I
  5. Convergence of CG – part II: local convergence (later – for the moment book and notes from class)
  6. Convergence of MINRES and GMRES
  7. Generalizations of (restarted) GMRES
  8. Methods based on the two-sided Lanczos algorithm
  9. Preconditioners based on incomplete factorizations
  10. Saddle-Point preconditioners
  11. Domain decomposition preconditioners - for convergence theory see notes from class)
  12. Multigrid 1 – basic iterative methods and error smoothing
  13. Multigrid 2 – smooth and oscillatory modes, basic multigrid
  14. Multigrid 3 – local mode analysis
  15. Multigrid 4 – convergence proof and analysis