Convergence of block triangular preconditioner for generalized saddle point matrices with highly singular (1,1) blocks

Abstract

In this paper, based on the preconditioners presented by Cao [J. Comput. Appl. Math. 2013;238:109–115], we present a block triangular preconditioner for generalized saddle point matrices whose coefficient matrices have singular (1,1) blocks. Moreover, theoretical analysis gives the eigenvalue distribution, forms of the eigenvectors and its minimal polynomial. Finally, numerical examples confirm our analysis when optimal parameters are chosen.