Conjugate gradient method with preconditioning by projector

Abstract

Preconditioning of the conjugate gradient method by a conjugate projector has been suggested. We describe an algorithm and prove its correctness. An estimate of the preconditioning effect in terms of the gap between the invariant subspace of smooth eigenvectors of a matrix of original system and the complement of the range of the preconditioning projector is obtained. The paper is supplied with results of a numerical experiment which suggest that the method may be efficient in practical computations.

Keywords:

• Conjugate gradient method
• preconditioning

AMS:

• 65F35
• 65F10
• 15A12