CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM

                  UNIVERSITY OF COLORADO AT DENVER



TITLE:   A Subspace Preconditioning Algorithm for Eigenvector/Eigenvalue
         Computation
 

SPEAKER: Andrew Knyazev, Department of Mathematics, UCD
         (Based on joint work with James H. Bramble and  Joseph E. Pasciak)

DATE:    Wednesday, September 20, 1995

PLACE:   Math Conference Room - Suite 540
         UCD Building, 1250 14th St., Denver

TIME:    2:30 pm (Refreshments served at 2:15 pm)



ABSTRACT

We consider the problem of computing a modest number of the 
smallest eigenvalues along with orthogonal bases for the
corresponding eigenspaces of a symmetric positive definite
operator defined on a finite dimensional real Hilbert space. 
In our applications, the dimension is large and the cost of 
inverting of the operator is prohibitive.  In this paper, we 
shall develop an  effective parallelizable  technique for
computing these eigenvalues and eigenvectors  utilizing subspace
iteration and preconditioning. Estimates will be provided which
show that the preconditioned  method converges linearly when used 
with a uniform preconditioner under the assumption that the 
approximating subspace is close enough to the span of desired  
eigenvectors.