A Comparison of the Preconditioners for the Large Symmetric Generalized Eigenvalue Problems by CG-type Methods

Abstract

Preconditioned Krylov subspace methods have proved to be efficient for computing the smallest eigenvalue of large symmetric generalized eigenvalue problem. As in the case of linear systems the success of these methods in many cases is due to the existence of good preconditioning techniques. In this paper we consider various preconditioners, such as ILU(0), ILU(k), ILUT(l, ), SSOR(Symmetric Successive OverRelaxation), and AGMG(AGgregate MultiGrid). We tested on the large sparse symmetric matrices arising from discretizations of PDE(Partial Differential Equation)s on structured grids. Our results show that ILUT gives the best performance for almost all of the problems tested.