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Book Chapter10.1007/978-3-0348-5501-3_10

Algorithms for Rational Discrete Least Squares Approximation Part I: Unconstrained Optimization

Peter Spellucci-1976-01-01-Birkhäuser Basel eBooks
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TL;DRAbstract

In this paper a modification of L. Wittmeyer’s method ([1], [14]) for rational discrete least squares approximation is given which corrects for its failure to converge to a non-optimal point in general. The modification makes necessary very little additional computing effort only. It is analysed thoroughly with respect to its conditions for convergence and its numerical properties. A suitable implementation is shown to be benign in the sense of F. L. Bauer [2]. The algorithm has proven successful even in adverse situations.

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In this paper a modification of L. Wittmeyer’s method ([1], [14]) for rational discrete least squares approximation is given which corrects for its failure to converge to a non-optimal point in general. The modification makes necessary very little additional computing effort only. It is analysed thoroughly with respect to its conditions for convergence and its numerical properties. A suitable implementation is shown to be benign in the sense of F. L. Bauer [2]. The algorithm has proven successful even in adverse situations.

Keywords

Convergence (economics)MathematicsMathematical optimizationPoint (geometry)Least-squares function approximationApplied mathematicsStatisticsEconomics

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