On the solution of symmetric linear systems by the preconditioned conjugate gradient method

Abstract

A class of preconditioning conjugate gradient methods is studied here. These methods are dependent on a relaxation parameter and are used in the solution of large linear system of equations Ax = b, where A is a symmetric positive definite matrix. The relaxed incomplete LL^T factorization (RILL^T ) and the relaxed block incomplete LL^T factorization (RBILL^T ) are studied here. Some numerical problems are solved and the optimum parameters values are evaluated. From these results the superiority of these, relative to others known methods, is clear.

Keywords:

• Symmetric linear system
• preconditioned gradient method
• relaxed incomplete LL^T factorization (RILL^T )
• relaxed block incomplete LL^T factorization (RBILL^T )

C.R Categories:

• G.1.3