Preconditioning for eigenproblems

Henk Van der Vorst

Department of Mathematics Utrecht University PO Box 80 010 NL-3508 TA Utrecht, The Netherlands


In the Jacobi-Davidson methods for eigenproblems a correction equation for the expansion of the search subspace is an important key for success. If the correction equation is solved accurately then we will have quadratic convergence of the eigenvalues, but unfortunately accurate solution by direct techniques will be far too expensive in actual situations. The usual approach is to solve the correction equation only approximately by some suitable method, in particular by a few steps of a preconditioned iterative solution method. Because of the projections that occur in the correction equation the inclusion of preconditioning is not so straightforward and we will discuss ways of including preconditioning in an efficient and stable manner. This is joint work with Gerard Sleijpen, Utrecht University.