CRPC-TR98747-S						April 1998

Title: Convergence Analysis of an Inexact Truncated RQ-Iteration

Author: Chao Yang

Submitted August 1998

Abstract:
The Truncated RQ-iteration (TRQ) can be used to calculate interior or
clustered eigenvalues of a large sparse and/or structured matrix A.  This
method requires solving a sequence of linear equations. When these
equations can be solved accurately by a direct solver, the convergence of
each eigenvalue is quadratic in general and cubic if A is hermitian.  An
important question is whether the TRQ iteration will still converge if
these equations are approximately solved by a preconditioned iterative
solver.  If it does converge, how fast is the convergence rate?  In this
paper, we analyze the convergence of an inexact TRQ iteration in which
linear systems are solved iteratively with some error. We show that under
some appropriate conditions, the convergence rate of the inexact TRQ is at
least linear with a small convergence factor.

------------------------------------------------------------------------------
Chao Yang
Department of Computational and Applied Mathematics
Rice University
y00chya@hstc.necsyl.com