Efficient Implementation of a Class of Preconditioned Conjugate Gradient Methods

Abstract

The preconditioned conjugate gradient (PCG) method is an effective means for solving systems of linear equations where the coefficient matrix is symmetric and positive definite. The incomplete $LDL^t $ factorizations are a widely used class of preconditionings, including the SSOR, Dupont-Kendall-Rachford, generalized SSOR, ICCG(0), and MICCG(0) preconditionings. The efficient implementation of PCG with a preconditioning from this class is discussed.