A Mesh Refinement Method for Ax = λBx

Abstact. The aim of this paper is to introduce a simple but efficient mesh refinement strategy for use with inverse iteration for finding one or a few solutions of an ordinary or partial differential eigenproblem of the form Ax = XBx. The focus is upon the case where A and B are symmetric and B is positive definite, although the approaches have a very broad application. A discussion of the combined use of mesh refinement and a correction scheme multigrid technique is also provided. The methods are illustrated by numerical results from experiments with two-point boundary value problems.