Transfinite interpolation on the medians of a triangle and best L 1-approximation期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Transfinite interpolation on the medians of a triangle and best L 1-approximation

Authors:	Petar Petrov Kurt Jetter

Affiliation:	(1) Department of Mathematics, University of Sofia, Blvd. James Boucher 5, 1164 Sofia, Bulgaria;(2) Institut für Angewandte Mathematik und Statistik, Universität Hohenheim, D-70593 Stuttgart, Germany

Abstract:	Let be a triangle in $mathbb{R}^{2} ,$ and let be the set of its three medians. We construct interpolants to smooth functions using transfinite (or blending) interpolation on The interpolants are of type f(₁)+g(₂)+h(₃), where (₁,₂,₃) are the barycentric coordinates with respect to the vertices of . Based on an error representation formula, we prove that the interpolant is the unique best L¹-approximant by functions of this type subject the function to be approximated is from a certain convexity cone in C³().Received: 17 December 2003

Keywords:	41A05 41A50 41A63 65D05
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