Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9506315 | Applied Mathematics and Computation | 2005 | 10 Pages |
Abstract
This paper presents a new method for obtaining a matrix M which is an approximate inverse preconditioner for a given matrix A, where the eigenvalues of A all either have negative real parts or all have positive real parts. This method is based on the approximate solution of the special Sylvester equation AXÂ +Â XAÂ =Â 2I. We use a Krylov subspace method for obtaining an approximate solution of this Sylvester matrix equation which is based on the Arnoldi algorithm and on an integral formula. The computation of the preconditioner can be carried out in parallel and its implementation requires only the solution of very simple and small Sylvester equations. The sparsity of the preconditioner is preserved by using a proper dropping strategy. Some numerical experiments on test matrices from Harwell-Boing collection for comparing the numerical performance of the new method with an available well-known algorithm are presented.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Amer Kaebi, Asghar Kerayechian, Faezeh Toutounian,