Optimizing two-level preconditionings for the conjugate gradient method

Abstract

The construction of efficient iterative linear equation solversfor ill-conditioned general symmetric positive definite systems is discussed.Certain known two-level conjugate gradient preconditioning techniquesare presented in a uniform way and are further generalized andoptimized with respect to the spectral or the K-condition numbers. Theresulting constructions have shown to be useful for the solution of largescaleill-conditioned symmetric positive definite linear systems.