Lecture 7 of 'Scientific Computing' (wi4201)

• The following subjects are discussed:
  
  
  • motivation for a series of linear systems (Newton Raphson method)
  • stopping criterion, possibilities, best choice
  • Jacobi iteration method
  • Gauss Seidel method
  • splitting methods, choice of M
  • converge proof Jacobi, row diagonal dominance
  • use the infinity norm of iteration matrix B
  • converge proof Gauss Seidel
  • use of truncated Neumann series
  • stencil notation for BIM
  • block Jacobi and Gauss Seidel method
  • fast tridiagonal solver for the blocks
  • acceleration, overrelaxation methods
  • convergence becomes slower if stepsize decreases
  • SOR has an order of magnitude faster convergence
    
    
• Material is described in pages 64 - 75 of the lecture notes. Recommended exercises: 5.9.4 - 5.9.14