A modified product preconditioner for indefinite and asymmetric generalized saddle-point matrices

In this paper, we present a new modified product preconditioner (MP) for a class of large sparse linear systems with indefinite and asymmetric matrices. The eigenvalue distribution and form of the eigenvectors of the presented new preconditioned matrix and its minimal polynomial are investigated. Some numerical experiments illustrate that the proposed new preconditioner performs better than block diagonal preconditioner, block triangular preconditioner, constraint preconditioner and product preconditioner.