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Approximation by piecewise constants on convex partitions

Davydov, O. (2012) Approximation by piecewise constants on convex partitions. Journal of Approximation Theory, 164 (2). pp. 346-352. ISSN 0021-9045

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Abstract

We show that the saturation order of piecewise constant approximation in Lp norm on convex partitions with N cells is N−2/(d+1), where d is the number of variables. This order is achieved for any on a partition obtained by a simple algorithm involving an anisotropic subdivision of a uniform partition. This improves considerably the approximation order N−1/d achievable on isotropic partitions. In addition we show that the saturation order of piecewise linear approximation on convex partitions is N−2/d, the same as on isotropic partitions.

Item type: Article
ID code: 40283
Keywords: approximation, convex partitions , mathematical analysis, isotropic partitions, Probabilities. Mathematical statistics, Analysis, Applied Mathematics, Mathematics(all), Numerical Analysis
Subjects: Science > Mathematics > Probabilities. Mathematical statistics
Department: Faculty of Science > Mathematics and Statistics
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Depositing user: Pure Administrator
Date Deposited: 02 Jul 2012 10:16
Last modified: 27 Mar 2014 10:14
URI: http://strathprints.strath.ac.uk/id/eprint/40283

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