Approximate inverse preconditioning for shifted linear systems

In this paper we consider the problem of preconditioning symmetric positive definite matrices of the form (A)\u3b1 = A + \u3b1I where \u3b1 > 0. We discuss how to cheaply modify an existing sparse approximate inverse preconditioner for A in order to obtain a preconditioner for A\u3b1. Numerical experiments illustrating the performance of the proposed approaches are presented