Numerical Stability of Lanczos Methods release_t6opaionf5cnjmtny5ozjykvem

by Eamonn Cahill, Alan Irving, Christopher Johnson, James Sexton

Released as a paper-conference .

1999  

Abstract

The Lanczos algorithm for matrix tridiagonalisation suffers from strong numerical instability in finite precision arithmetic when applied to evaluate matrix eigenvalues. The mechanism by which this instability arises is well documented in the literature. A recent application of the Lanczos algorithm proposed by Bai, Fahey and Golub allows quadrature evaluation of inner products of the form ψ^† g(A) ψ. We show that this quadrature evaluation is numerically stable and explain how the numerical errors which are such a fundamental element of the finite precision Lanczos tridiagonalisation procedure are automatically and exactly compensated in the Bai, Fahey and Golub algorithm. In the process, we shed new light on the mechanism by which roundoff error corrupts the Lanczos procedure
In text/plain format

Archived Files and Locations

application/pdf  81.7 kB
file_bjssc3d6jnaehn5mfpeo6hdl7m
archive.org (archive)
arxiv.org (repository)
web.archive.org (webarchive)
core.ac.uk (web)
Read Archived PDF
Preserved and Accessible
Type  paper-conference
Stage   submitted
Date   1999-09-17
Version   v1
Language   en ?
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: ecf4efbf-246b-4c03-b751-ec4fab21a1e7
API URL: JSON