Lecture 6 of 'Scientific Computing' (wi4201)

• The following subjects are discussed:
  
  
  • Partial pivotting, complete pivotting
  • Solve PA = LU and PA u = Pf
  • Example partial pivotting
  • When is partial pivotting needed?
  • A is SPD, Cholesky decomposition
  • Partial pivotting is not needed if A is SPD
  • Band matrices, sparse matrices
  • Unstructured grid, profile method
  • Iterative refinement
  • Double precision, single precision
  • Basic Iterative Methods (BIM)
  • error and residual
  • splitting of matrix A
  • convergence, error iteration, iteration matrix
  • Richardson method, spectral radius
  • spectral radius less than 1 for fast convergence
    
    
• Material is described in pages 11 and 12, 51 - 64 of the lecture notes. Recommended exercises: 4.13.5 - 4.13.7 and 5.9.1 - 5.9.3