Lecture 12 of 'Scientific Computing' (wi4201)

• The following subjects are discussed:
  
  
  • Recap properties preconditioner
  • BIM as preconditioner, be careful that the matrix M should be SPD
  • Use Symmetric SOR (SSOR) instead of SOR
  • The band of the Choleski factor is full, due to fill in
  • Incomplete Choleski removes all or part of the fill in
  • Historical remarks about ICCG (Incomplete Choleski CG)
  • How to compute the Incomplete Choleski factor in an efficient way
  • ICCG(0) and ICCG(3) compared
  • Superlinear convergence and eigenvalues of the preconditioned matrix
  • Modified IC preconditioner
  • Krylov methods for a general non-singular matrix
  • No method exists with all nice properties of CG for a general non-singular matrix
  • Three classes of methods: CGNR, Bi-CGSTAB, and GMRES
  • Details of CGNR, CG applied to the normal equations
  • Properties of CGNR
    
    
• Material is described in pages 108-118 of the lecture notes. Recommended exercises: 7.2.1 - 7.2.4