Lecture 13 of 'Scientific Computing' (wi4201)

• The following subjects are discussed:
  
  
  • For general non-singular matrices there are 3 classes of Krylov methods
  • Bi-CG can be motivated from a larger system using A and A transpose
  • the residual and shadow residuals are bi-orthogonal
  • properties of Bi-CG, short recurrences, not robust, round off errors
  • always compare the updated residual at the end with the exact residual
  • more efficient variants: CGS and Bi-CGSTAB (Delft products)
  • GMRES, GCR are equivalent
  • properties of GMRES: robust, optimal convergence, long recurrences
  • convergence proof, super linear convergence
  • amount of work, amount of memory
  • restarting and truncation
  • hybrid methods: GMRESR and IDR(s) (Delft products)
  • How to choose the best Krylov method
    
    
• Material is described in pages 118-126 of the lecture notes and slides .
  Recommended exercises: 7.3.1 - 7.3.6