On the eigenvalue distribution of preconditioned nonsymmetric saddle point matrices

Abstract

SUMMARY In this paper, we derive bounds for the complex eigenvalues of a nonsymmetric saddle point matrix with a symmetric positive semidefinite (2,2) block, that extend the corresponding previous bounds obtained by Bergamaschi. For the nonsymmetric saddle point problem, we propose a block diagonal preconditioner for the conjugate gradient method in a nonstandard inner product. Numerical experiments are also included to test the performance of the presented preconditioner. Copyright © 2013 John Wiley & Sons, Ltd.