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A direct method for a regularized least-squares problem
Linköpings universitet, Matematiska institutionen, Beräkningsvetenskap. Linköpings universitet, Tekniska högskolan.
Linköpings universitet, Matematiska institutionen, Beräkningsvetenskap. Linköpings universitet, Tekniska högskolan.
2009 (engelsk)Inngår i: NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, ISSN 1070-5325, Vol. 16, nr 8, s. 649-675Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

We consider a linear system of the form A(1)x(1)+A(2)X(2)+eta=b1. The vector eta consists of identically distributed random variables all with mean zero. The unknowns are split into two groups x(1) and x(2). In the model usually there are more unknowns than observations and the resulting linear system is most often consistent having an infinite number of solutions. Hence some constraint on the parameter vector x is needed. One possibility is to avoid rapid variation in, e.g. the parameters x(2). We formulate the problem as a partially regularized least-squares problem, and propose a direct solution method based on the QR decomposition of matrix blocks. Further we consider regularizing using one and two regularization parameters, respectively. We also discuss the choice of regularization parameters, and extend Reinschs method to the case with two parameters. Also the cross-validation technique is treated. We present test examples taken from an application in modelling of the substance transport in rivers.

sted, utgiver, år, opplag, sider
2009. Vol. 16, nr 8, s. 649-675
Emneord [en]
QR-factorization, block matrices, least squares, regularization parameter, cross-validation, Reinschs method
HSV kategori
Identifikatorer
URN: urn:nbn:se:liu:diva-19993DOI: 10.1002/nla.644OAI: oai:DiVA.org:liu-19993DiVA, id: diva2:232442
Tilgjengelig fra: 2009-08-24 Laget: 2009-08-24 Sist oppdatert: 2009-08-24

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  • de-DE
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