The multi-grid preconditioned conjugate gradient method

Osamu Tatebe

Dept. of Info. Sci., Fac. of Sci., the University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan


Abstract

A multi-grid preconditioned conjugate gradient method(MGCG method), which uses the multi-grid method as a preconditioner of the PCG method, is proposed. The multi-grid method has inherent high parallelism and fast convergence of long wave length components, which is important in iterative methods. By using this method as a preconditioner of the PCG method, an efficient method with high parallelism and fast convergence is obtained. First, it is shown that the multi-grid method satisfies the requirements of the preconditioner of the PCG method. Then numerical experiments show the MGCG method is superior to the ICCG method and the multi-grid method in point of fast convergence and high parallelism. Next the eigenvalue analysis theoretically bases the fast convergence and shows the multi-grid preconditioner is a desirable preconditioner.