Solution of f (A)x = b with projection methods for the matrix A

Abstract. In this paper, we expand on an idea for using Krylov subspace information for the matrix A and the vector b. This subspace can be used for the approximate solution of a linear system f(A)x = b, where f is some analytic function. We will make suggestions on how to use this for the case where f is the matrix sign function. 1 Introduction The matrix sign function plays an important role in QCD computations, see for instance [12]. In the computational models one has to compute an approximate solution for linear systems of the type (B + sign(A))x = b; (1) with A; B 2 C n\Theta n, and A and B do not commute. The latter property is an important bottleneck for the efficient computation of subspaces that can be used for the reduction of both A and B