Davydov, O. (2012) Approximation by piecewise constants on convex partitions. Journal of Approximation Theory, 164 (2). pp. 346-352. ISSN 0021-9045
Full text not available in this repository. (Request a copy from the Strathclyde author)Official URL: http://dx.doi.org/10.1016/j.jat.2011.11.001
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 |
| Subjects: | Science > Mathematics > Probabilities. Mathematical statistics |
| Department: | Faculty of Science > Mathematics and Statistics |
| Related URLs: | |
| Depositing user: | Pure Administrator |
| Date Deposited: | 02 Jul 2012 10:16 |
| Last modified: | 03 Aug 2012 10:04 |
| URI: | http://strathprints.strath.ac.uk/id/eprint/40283 |
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