Modified block preconditioner for generalized saddle point matrices with highly singular(1,1) blocks

ABSTRACT

In this paper, based on the preconditioners presented by Zhang [A new preconditioner for generalized saddle matrices with highly singular(1,1) blocks. Int J Comput Maths. 2014;91(9):2091-2101], we consider a modified block 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 the minimal polynomial. Finally, numerical examples show the eigenvalue distribution with the presented preconditioner and confirm our analysis.