A Note on the SIMPLE Preconditioner for Nonsymmetric Saddle Point Problems
Authors
Jianlei Li, Zhijiang Zhang and Liang Li
Abstract
The eigenvalue analysis of the SIMPLE preconditioner for solving two-by-two block linear
equations with the (1, 2)-block being the transpose of the (2, 1)-block and the (2, 2)-block being zero was
investigated in Li and Vuik [Numer Lin. Alg. Appl., 2004, 11:511-523]. In this note, we extend their ideas by
allowing the (1, 2)-block to be not equal to the transpose of the (2, 1)-block and investigate the relationship
of the two different formulations spectrum of the SIMPLE preconditioned matrix by using the theory of
matrix eigenvalue. And also the SIMPLE type methods are given.