A Flexible Preconditioned Arnoldi Method for Shifted Linear Systems

Abstract

We are interested in the numerical solution of the large nonsymmetric shifted linear system, $(A + \alpha I) x = b$, for many different values of the shift $\alpha$ in a wide range. We apply the Saad's flexible preconditioning technique [14] to the solution of the shifted systems. Such flexible preconditioning with a few parameters could probably cover all the shifted systems with the shift in a wide range. Numerical experiments report the effectiveness of our approach on some problems.