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Iterative refinement for constrained and weighted linear least squares
Responsible organisation
1994 (English)In: Bit: numerical mathematics, ISSN 0006-3835, Vol. 34, no 2, 239-253 p.Article in journal (Refereed) Published
Abstract [en]

We present an algorithm for mixed precision iterative refinement on the constrained and weighted linear least squares problem, the CWLSQ problem. The approximate solution is obtained by solving the CWLSQ problem with the weightedQR factorization [6]. With backward errors for the weightedQR decomposition together with perturbation bounds for the CWLSQ problem we analyze the convergence behaviour of the iterative refinement procedure. In the unweighted case the initial convergence rate of the error of the iteratively refined solution is determined essentially by the condition number. For the CWLSQ problem the initial convergence behaviour is more complicated. The analysis shows that the initial convergence is dependent both on the condition of the problem related to the solution,x, and the vector lambda=Wr, whereW is the weight matrix andr is the residual. We test our algorithm on two examples where the solution is known and the condition number of the problem can be varied. The computational test confirms the theoretical results and verifies that mixed precision iterative refinement, using the system matrix and the weightedQR decomposition, is an effective way of improving an approximate solution to the CWLSQ problem.

Place, publisher, year, edition, pages
1994. Vol. 34, no 2, 239-253 p.
Keyword [en]
Iterative refinement - error analysis - least squares - QR decomposition - weights
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-3983Local ID: 4399OAI: oai:DiVA.org:miun-3983DiVA: diva2:29015
Available from: 2008-09-30 Created: 2009-09-21Bibliographically approved

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Gulliksson, Mårten
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  • apa
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