Preconditioned conjugate gradient method: Difference between revisions

Revision as of 23:37, 12 July 2008

Revision as of 12:39, 19 September 2008

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ToPossible savepreconditioners computional time it is important to take a symmetric preconditioner. This can beare Jacobi, symmetric Gauss-Seidel or Symmetric Successive Over Relaxation (SSOR).

To save computional time it is important to take a symmetric preconditioner. This can be Jacobi, symmetric Gauss-Seidel or Symmetric Successive Over Relaxation (SSOR).

The simplest preconditioner is a diagonal matrix that has just the diagonal elements of <math>A</math>. This is known as Jacobi preconditioning or diagonal scaling. Since diagonal matrices are trivial to invert and store in memory, a diagonal preconditioner is a good starting point. More sophisticated choices must trade-off the reduction in <math>\kappa(A)</math>, and hence faster convergence, with the time spent computing <math>P^{-1}</math>.