Analysis

• When the iteration converges, we have

  

• When does it converge?
  • Depends on the splitting.
  • Jacobi and Gauss-Seidel will work for symmetric and positive-definite matrices (defined in CLR Ch. 31.1).
• Why iterative method?
  • Easier to implement.
  • Sometimes, an iterative method can be much faster than a direct method, i.e., PLU-factorization.