Preconditioned conjugate gradient method: Difference between revisions

Revision as of 15:28, 26 September 2007

Revision as of 16:14, 12 October 2007

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:<math>A x= b.\,</math>

where <math>A</math> is symmetric [positive definite]. If the [[Matrix (mathematics)|matrix]] <math>A</math> is [[ill-conditioned]], i.e. it has a large [[condition number]] <math>\kappa(A)</math>, it is often useful to use a [[preconditioner|preconditioning matrix]] <math>P^{-1}</math> that is chosen such that <math>P^{-1} \approx A^{-1}</math> and solve the system

:<math> P^{-1}Ax = P^{-1}b,\,</math>