Title: Generalizations of an Inverse Free Preconditioned Algorithm for Symmetric Generalized Eigenvalue Problems

Speaker: Pat Quillen, University of Kentucky

Date/Time: April 20th, 2005, 9:00-10:00 am

Location: Building 980, Room 95 (Sandia NM)

Brief Abstract: In their 2002 paper, Golub and Ye present an inverse free preconditioned Krylov subspace method for computing the extreme eigenvalues of a symmetric definite pencil (A,B). In this talk we discuss application of this algorithm to a symmetric definite pencil (C,D) whose extreme eigenvalues correspond to eigenvalues of the pencil (A,B) nearest to some target µ. In general, convergence of the algorithm applied to this transformed pencil is prohibitively slow and a high quality preconditioner is required. Our focus is largely on preconditioning techniques for this problem, and this will be the basis for much of the discussion. We also discuss a block generalization of the inverse free algorithm which exhibits convergence behavior superior to that of the original algorithm, especially when combined with a preconditioning strategy. Examples will be provided demonstrating the viability of this method.

CSRI POC: Jonathan Hu, (925) 294-2931