Lecture 8 of 'Scientific Computing' (wi4201)

• The following subjects are discussed:
  
  
  • Wrap up of Lecture 1 to 7
  • Convergence of Jacobi and Gauss Seidel for diagonal dominant matrices
  • Linear convergence, spectral radius
  • Jacobi with relaxation or damping, eigenvalues of the iteration matrix
  • If step size becomes small number of iterations increases
  • Defect correction, splitting and preconditioning
  • Multigrid method, fine grid, coarse grid
  • High and low frequency eigenvalues and eigenvectors
  • Damped Jacobi slow convergence for low frequency eigenvalues
  • Damped Jacobi fast convergence for high frequency eigenvalues
  • smoothing behaviour of damped Jacobi
    
    
• Material is described in pages 81 - 83 and 88 - 90 of the lecture notes.
  
  
• Typo's
  
  
  • Page 72 In the proof of Theorem 5.4.2: the 1-norm should everywhere be replaced by the infinity-norm.