A proposal of Preconditioning based on AGM (Arithmetic-Geometric Mean) of Eigenvalues(Algorithms for Matrix/Eigenvalue Problems and their Applications,<Special Issue>Joint Symposium of JSIAM Activity Groups 2008)

Abstract

In this paper, we propose a new preconditioning technique based on AGM (Arithmetic-Geometric Mean) of eigenvalues by means of determination of approximate one. Through numerical experiments, we examine distribution of eigenvalues, and verify effectiveness and parallelism of Conjugate Gradient method with our proposed preconditioning on SMP machine with shared memory compared with the conventional preconditioned CG method.