Options
Improved componentwise verified error bounds for least squares problems and underdetermined linear systems
Publikationstyp
Journal Article
Date Issued
2013-07-11
Sprache
English
Author(s)
Institut
TORE-URI
Journal
Volume
66
Issue
2
Start Page
309
End Page
322
Citation
Numerical Algorithms 2 (66): 309-322 (2014)
Publisher DOI
Scopus ID
Publisher
Springer Science Business Media B.V.
Recently Miyajima presented algorithms to compute componentwise verified error bounds for the solution of full-rank least squares problems and underdetermined linear systems. In this paper we derive simpler and improved componentwise error bounds which are based on equalities for the error of a given approximate solution. Equalities are not improvable, and the expressions are formulated in a way that direct evaluation yields componentwise and rigorous estimates of good quality. The computed bounds are correct in a mathematical sense covering all sources of errors, in particular rounding errors. Numerical results show a gain in accuracy compared to previous results. © 2013 Springer Science+Business Media New York.
Subjects
Componentwise error estimates
Extra-precise residual evaluation
INTLAB
Least squares problems
Normal equations
Underdetermined linear systems
DDC Class
510: Mathematik