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A higher order approximation technique for restricted linear least-squares problems

Published online by Cambridge University Press:  17 April 2009

Heinz W. Engl  and
C.W. Groetsch
Heinz W. Engl
Affiliation:
Institut fr Mathematik, Universitt, A-9022 KLAGENFURT, Austria. Institut fr Mathematik, Johannes-Kepler-UniversittA-4040 LINZ, Austria
C.W. Groetsch
Affiliation:
Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH. 45221-0025, U.S.A.
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Abstract

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An essential limitation for the method of weighting for equality constrained linear least-squares problems is the sub-optimality of the attainable convergence rate. In this paper, we propose a method, related to the method of iterated Tikhonov regularisation, that (under suitable conditions) gives rise to convergence rates which are arbitrarily near the optimal rate. As a by-product, we develop the theory of iterated Tikhonov regularisation for equations with unbounded linear operators.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 37 , Issue 1 , February 1988 , pp. 121 - 130
Copyright
Copyright Australian Mathematical Society 1988

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