On Some New Approximate Factorization Methodsfor Block Tridiagonal Matrices Suitable Forrnvector And Parallel Processors

摘要

In this paper, to obtain an efficient parallel algorithm to solve sparse bloek-tridiagonal linear systems, stair matrices are used to construct some parallel polynomial approximate inverse preconditioners. These preconditioners are suitable when the desired goal is to maximize parallelism. Moreover, some theoretical results concerning these preconditioners are presented and how to construct preconditioners effectively for any nonsingular block tridiagonal H-matrices is also described. In addition, the validity of these preconditioners is illustrated with some numerical experiments arising from the second order elliptic partial differential equations and oil reservoir simulations.