Approximate Inverse Preconditioners for solving Toeplitz matrices

摘要

In this paper, we give the upper bounds for inverse elements of strictly diagonally dominant pentadiagonal matrix, and improve the bounds in [SIAM. J. matrix Anal. Appl. 20 (1999) 820-837],especially, as the pentadiagonal matrix is M-matrix, we give the exact inverse. Numerical experiments show that the approximate inverse is a very effective preconditioner, when the approximate inverse be used as a preconditioner to solve the banded Toeplitz matrix.