The Construction of Parallel Preconditioner in Preconditioned Conjugate Gradient Method

In this paper, we study the problem of solving the band linear systems on distributed memory multi-computer, and emphasis on the research of preconditioned conjugate gradient method. By reconstructing the preconditioner of traditional preconditioned conjugate gradient method, We gain the preconditioner suiting for parallel computation. The efficiency of Conjugate Gradient Method is improved while preserving the parallelism. Moreover, three examples have been implemented on Linux Networx cluster, and the numerical experiments indicate that our algorithm is feasible and effective.