UNIVERSITY OF COLORADO AT DENVER

PLACE: Mathematics Conference Room 626 UCD Building, 1250 14th St., Denver

TIME: NOON (Refreshments served at 11:45 am)

DATE: April 17, 2000

Zlatko Drmac 
Department of Mathematics
University of Zagreb
Croatia

Title: 
Perturbation theory and iterative symmetric eigensolvers

Abstract: 

To find only a few eigenpairs of large symmetric matrix, one 
usually constructs a sequence of low-dimensional subspaces and 
hopes to approximate the target eigenpairs from these subspaces. 
To be successful in designing efficient algorithms, one needs to 
know 
(i)   how good is the current subspace, e.g. how accurate are the 
      Ritz pairs
(ii)  how to enrich the current subspace with directions close to the 
      target vectors
(iii) how to compute accurate Rayleigh quotient matrix and the 
      Ritz pairs in finite precision arithmetic.
Sharp computable bounds assure fast convergence, good stopping 
criterion and accurate approximations. We discuss these issues in the 
framework of the perturbation theory. We also show how the perturbation
theory approach sheds a new light on some well-known methods and 
improves the understandig of their behaviour.