BibTeX
@MISC{Meerbergen00thelanczos,
author = {Karl Meerbergen},
title = {The Lanczos method with semi-inner product},
year = {2000}
}
Bookmark
 |
 |
 |
 |
 |
 |
OpenURL
Abstract
The spectral transformation Lanczos method is very popular for solving large scale Hermitian generalized eigenvalue problems. The method uses a special inner product so that the symmetric Lanczos method can be used. Sometimes, a semi-inner product must be used. This may lead to instabilities and break-down. In this paper, we suggest a cure for breakdown by use of an implicit restart in the Lanczos method. Keywords: Lanczos method, semi-inner product, implicit restart AMS (MOS) subject classifications: 65F15,65F50 Computational Science and Engineering Department Atlas Centre Rutherford Appleton Laboratory Oxon OX11 0QX March 31, 2000 Contents 1 Introduction 1 2 Analysis of the eigenvalue problem 2 3 The spectral transformation Lanczos method 3 4 Analysis 5 4.1 A bound for the two-norm of the Lanczos vectors . . . . . . . . . . . . . 6 4.2 Analysis of the Lanczos recurrence relation . . . . . . . . . . . . . . . . . 7 4.3 Analysis for the implicit restart . . . . . . . . . . . . . ....
