Preprint No. MPIMD/13-04

Title: Tuned preconditioners for inexact two-sided inverse and Rayleigh quotient iteration

Author(s): Melina Freitag, Patrick K├╝rschner

Email: kuerschner@mpi-magdeburg.mpg.de

Date: 2013-04-23

Abstract:

Convergence results are provided for inexact two-sided inverse and Rayleigh quotient iteration, which extend the previously established results to the generalized eigenproblem, and inexact solves with a decreasing solve tolerance. Moreover, the simultaneous solution of the forward and adjoint problem arising in two-sided methods is considered and the successful tuning strategy for preconditioners is extended to two-sided methods. Furthermore, it is shown that inexact two-sided Rayleigh quotient iteration and the inexact two-sided Jacobi-Davidson method (without subspace expansion) applied to the generalized preconditioned eigenvalue problem are equivalent when a certain number of steps of a Petrov-Galerkin-Krylov method is used, and when this specific tuning strategy is applied.

BibTeX:

@TECHREPORT{MPIMD13-04,
author = {Melina Freitag and Patrick K├╝rschner},
title = {Tuned preconditioners for inexact two-sided inverse and Rayleigh quotient iteration},
number = {MPIMD/13-04},
month = apr,
year = 2013,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{http://www.mpi-magdeburg.mpg.de/preprints/}},
}


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