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Title: On the Convergence of an Implicitly Restarted Arnoldi Method

Abstract

We show that Sorensen's [35] implicitly restarted Arnoldi method (including its block extension) is simultaneous iteration with an implicit projection step to accelerate convergence to the invariant subspace of interest. By using the geometric convergence theory for simultaneous iteration due to Watkins and Elsner [43], we prove that an implicitly restarted Arnoldi method can achieve a super-linear rate of convergence to the dominant invariant subspace of a matrix. Moreover, we show how an IRAM computes a nested sequence of approximations for the partial Schur decomposition associated with the dominant invariant subspace of a matrix.

Authors:
Publication Date:
Research Org.:
Sandia National Labs., Albuquerque, NM (US); Sandia National Labs., Livermore, CA (US)
Sponsoring Org.:
US Department of Energy (US)
OSTI Identifier:
9021
Report Number(s):
SAND99-1756J
TRN: AH200122%%138
DOE Contract Number:  
AC04-94AL85000
Resource Type:
Journal Article
Journal Name:
SIAM Journal on Matrix Analysis and Its Applications
Additional Journal Information:
Other Information: Submitted to SIAM Journal on Matrix Analysis and Its Applications; PBD: 12 Jul 1999
Country of Publication:
United States
Language:
English
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; CONVERGENCE; EIGENVALUES; ITERATIVE METHODS; MATRIX ELEMENTS; SIMULTANEOUS ITERATION; ARNOLDI REDUCTION; SCHUR DECOMPOSITION; RESTARTING; EIGEN-VALUES

Citation Formats

Lehoucq, Richard B. On the Convergence of an Implicitly Restarted Arnoldi Method. United States: N. p., 1999. Web.
Lehoucq, Richard B. On the Convergence of an Implicitly Restarted Arnoldi Method. United States.
Lehoucq, Richard B. Mon . "On the Convergence of an Implicitly Restarted Arnoldi Method". United States. https://www.osti.gov/servlets/purl/9021.
@article{osti_9021,
title = {On the Convergence of an Implicitly Restarted Arnoldi Method},
author = {Lehoucq, Richard B},
abstractNote = {We show that Sorensen's [35] implicitly restarted Arnoldi method (including its block extension) is simultaneous iteration with an implicit projection step to accelerate convergence to the invariant subspace of interest. By using the geometric convergence theory for simultaneous iteration due to Watkins and Elsner [43], we prove that an implicitly restarted Arnoldi method can achieve a super-linear rate of convergence to the dominant invariant subspace of a matrix. Moreover, we show how an IRAM computes a nested sequence of approximations for the partial Schur decomposition associated with the dominant invariant subspace of a matrix.},
doi = {},
journal = {SIAM Journal on Matrix Analysis and Its Applications},
number = ,
volume = ,
place = {United States},
year = {1999},
month = {7}
}