Davydov, O. (2012) Approximation by piecewise constants on convex partitions. Journal of Approximation Theory, 164 (2). pp. 346-352. ISSN 0021-9045Full text not available in this repository. (Request a copy from the Strathclyde author)
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.
|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|
|Depositing user:||Pure Administrator|
|Date Deposited:||02 Jul 2012 09:16|
|Last modified:||07 Jan 2017 01:14|