Incomplete factorization for preconditioning shifted linear systems

Abstract

We consider the preconditioning of linear systems with matrices depending on a parameter, i.e., A εχ ε = b ε with A ε = M + εN symmetric positive definite. Instead of using extreme strategies as to apply the same preconditioner along the process, or on the contrary, to compute a different preconditioner for each value of ", we propose an intermediate technique. It is based on the construction of one initial preconditioner from an incomplete factorization of M, which can be easily updated for each value of " at a low computational cost. Several numerical experiments are presented in order to show the efficiency of the proposed preconditioner.