Abstract
We consider solving the large linear systems involving a matrix which has a relatively large number of small nonzero elements. As suitable preconditionings for Krylov subspace methods to solve such linear systems, the techniques using sparse direct solvers for a sparse approximate coefficient matrix have been proposed. The sparse approximate coefficient matrix is generated by the so-called cutoff, and the performance of the preconditioning is highly dependent on the cutoff parameter. In this paper, we present a technique to suitably estimate a cutoff parameter. The validity of our technique is verified by some numerical experiments.
