Preconditioned Conjugate Gradients

• Notation:
  • solving Ax = b
  • is initial guess
  • r is residual
• Algorithm:

  compute M if necessary
  
  solve
  z = p
  
  for i = 0, 1, ..., until convergence:
  

• Notes:
  • matrix-vector multiplication each iteration
  • preconditioning solve each iteration
  • preconditioner M should in some sense approximate A