Computer Science NASC Seminar

Efficient Inexact Rayleigh Quotient Iteration and its Connections to the Jacobi-Davidson Method

Fei Xu, Temple University

March 25, 2011 10:00AM
Warren Weaver Hall, Room 1302
251 Mercer Street
New York, NY, 10012-1110

Spring 2011 NASC Seminars Calendar


We study inexact Rayleigh quotient iteration (IRQI) for
computing a simple interior eigenpair of the generalized eigenvalue
problem Av = \lambda Bv, providing new insights into three aspects of
a special type of preconditioners with “tuning” for the efficient
solution of the shifted linear systems arising in this algorithm. We
?rst show that full asymptotic convergence rates of IRQI can be
achieved, if the shifted linear systems are solved by a Krylov
subspace method with a tuned preconditioner to a moderately small ?xed
tolerance. We also discuss the equivalence of the inner solves of IRQI
and the single-vector Jacobi-Davidson method. A ?exible GMRES (FGMRES)
algorithm with a special con?guration in the ?rst inner step is
proposed to simplify the use of tuning, and is shown to be as
efficient as GMRES with the tuned preconditioner. The success of this
FGMRES is also explained by its connection to the Jacobi-Davidson

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