Least Squares Methods to Minimize Errors in a Smooth, Strictly Convex Norm on [formula omitted]m

An algorithm for computing solutions of overdetermined systems of linear equations in n real variables which minimize the residual error in a smooth, strictly convex norm in a finite dimensional space is given. The algorithm proceeds by finding a sequence of least squares solutions of suitably modif...

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Bibliographic Details
Published inJournal of approximation theory Vol. 73; no. 2; pp. 180 - 198
Main Authors Owens, R.W., Sreedharan, V.P.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 1993
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Summary:An algorithm for computing solutions of overdetermined systems of linear equations in n real variables which minimize the residual error in a smooth, strictly convex norm in a finite dimensional space is given. The algorithm proceeds by finding a sequence of least squares solutions of suitably modified problems. Most of the time, each iteration involves one line search for the root of a nonlinear equation, though some iterations do not have any root seeking line search. Convergence of the algorithm is proved, and computational experience on some numerical examples is also reported.
ISSN:0021-9045
1096-0430
DOI:10.1006/jath.1993.1037