Subspace iterative methods for eigenvalue problems

This paper presents novel perturbation bounds for generalized symmetric positive definite eigenvalue problems. The bounds provide the insights for an observed computational phenomenon that is not easily explained by the existing bounds developed previously. Using the new bounds, we provide an analysis of a subspace Newton type procedure for computing a few extreme eigenpairs for generalized symmetric positive definite systems. A preconditioned version of this subspace iterative method is also studied. © 1999 Elsevier Science Inc. All rights reserved.