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Modifying the $QR$-decomposition to constrained and weighted linear least squares
Responsible organisation
1992 (English)In: SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, Vol. 13, no 4, 1298-1313 p.Article in journal (Refereed) Published
Abstract [en]

A new way of looking at a class of methods for the weighted linear least squares problem $min _x | M^{ - ( 1/2 )} ( b - Ax ) |_2 $ where $M = {operatorname{diag}}(mu _i )$ is presented by introducing a modified QR-decomposition with $Q$$M$-invariant, i.e., $QMQ^T = M$. One of the main advantages with this approach is that linear constraints are easily incorporated by letting the corresponding diagonal elements in $M$ become zero. Householder reflections are generalized to $M$-invariant reflections, and an algorithm for solving the constrained and weighted linear least squares problem is described. The system equations (or the augmented system equations) are used to derive condition numbers, and the connection between these condition numbers and the rounding error in the solution is investigated.

Place, publisher, year, edition, pages
1992. Vol. 13, no 4, 1298-1313 p.
Keyword [en]
least squares, weights, constraints, QR-decomposition, condition numbers, stability
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-3984Local ID: 4400OAI: oai:DiVA.org:miun-3984DiVA: diva2:29016
Available from: 2008-09-30 Created: 2009-09-21Bibliographically approved

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Gulliksson, Mårten
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  • apa
  • harvard1
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Output format
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