Approximation by piecewise constants on convex partitions

作者：Davydov Oleg^*

来源：Journal of Approximation Theory, 2012, 164(2): 346-352.

DOI：10.1016/j.jat.2011.11.001

We show that the saturation order of piecewise constant approximation in L p 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 f is an element of W-p(2)(Omega) on a partition obtained by a simple algorithm involving an anisotropic subdivision of a uniform partition. This improves considerably the approximation order N lid 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.

• 出版日期2012-2