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Computable backward error bounds for basic algorithms in linear algebra
Publikationstyp
Journal Article
Date Issued
2015-07-01
Sprache
English
Author(s)
Institut
TORE-URI
Volume
6
Issue
3
Start Page
360
End Page
363
Citation
Nonlinear Theory and Its Applications, IEICE 3 (6): 360-363 (2015)
Publisher DOI
Standard error estimates in numerical linear algebra are often of the form γk|R||S| where R,S are known matrices and γk:=ku/(1-u) with u denoting the relative rounding error unit. Recently we showed that for a number of standard problems γk can be replaced by ku for any order of computation and without restriction on the dimension. Such problems include LU- and Cholesky decomposition, triangular system solving by substitution, matrix multiplication and more. The theoretical bound implies a practically computable bound by estimating the error in the floating-point computation of ku|R||S|. Standard techniques, however, imply again a restriction on the dimension. In this note we derive simple computable bounds being valid without restriction on the dimension. As the bounds are mathematically rigorous, they may serve in computer assisted proofs.
DDC Class
004: Informatik
510: Mathematik
More Funding Information
This research was supported by CREST, JST.