miun.sePublikationer
Ändra sökning
RefereraExporteraLänk till posten
Permanent länk

Direktlänk
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
On the modified Gram-Schmidt algorithm for weighted and constrained linear least squares problems.
Ansvarig organisation
1995 (Engelska)Ingår i: Bit: numerical mathematics, ISSN 0006-3835, Vol. 35, nr 4, s. 453-468Artikel i tidskrift (Refereegranskat) Published
Abstract [en]

A framework and an algorithm for using modified Gram-Schmidt for constrained and weighted linear least squares problems is presented. It is shown that a direct implementation of a weighted modified Gram-Schmidt algorithm is unstable for heavily weighted problems. It is shown that, in most cases it is possible to get a stable algorithm by a simple modification free from any extra computational costs. In particular, it is not necessary to perform reorthogonalization. Solving the weighted and constrained linear least squares problem with the presented weighted modified Gram-Schmidt algorithm is seen to be numerically equivalent to an algorithm based on a weighted Householder-likeQR factorization applied to a slightly larger problem. This equivalence is used to explain the instability of the weighted modified Gram-Schmidt algorithm. If orthogonality, with respect to a weighted inner product, of the columns inQ is important then reorthogonalization can be used. One way of performing such reorthogonalization is described. Computational tests are given to show the main features of the algorithm.

Ort, förlag, år, upplaga, sidor
1995. Vol. 35, nr 4, s. 453-468
Nyckelord [en]
Gram-Schmidt - error analysis - least squares - QR factorization - weights
Nationell ämneskategori
Matematik
Identifikatorer
URN: urn:nbn:se:miun:diva-3980Lokalt ID: 4397OAI: oai:DiVA.org:miun-3980DiVA, id: diva2:29012
Tillgänglig från: 2008-09-30 Skapad: 2009-09-21Bibliografiskt granskad

Open Access i DiVA

Fulltext saknas i DiVA

Personposter BETA

Gulliksson, Mårten

Sök vidare i DiVA

Av författaren/redaktören
Gulliksson, Mårten
Matematik

Sök vidare utanför DiVA

GoogleGoogle Scholar

urn-nbn

Altmetricpoäng

urn-nbn
Totalt: 151 träffar
RefereraExporteraLänk till posten
Permanent länk

Direktlänk
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annat format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annat språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf