Bivariate polynomial interpolation on the square at new nodal sets
type: Item
instance of: scholarly article
title: Bivariate polynomial interpolation on the square at new nodal sets
zbMATH Open document ID: 1081.41001
author: M. Caliari
author: Marco Vianello
author: Stefano De Marchi
published in: Applied Mathematics and Computation
publication date: 2005-06-13T00:00:00Z
review text: Let \(\Omega\) be a compact from \({\mathbb R}^d\). Set \(X_N^*\) from \(\Omega\) of cardinality \(N\) is called an optimal polynomial interpolation points, if \(\Lambda_n(X_N)=\max_{x\in\Omega}\sum_{i=1}^N| l_i({\mathbf x},X_N)| \) attains it's minimum on \(X_N^*\). Here \(X_N=\{{\mathbf x}_1,\ldots,{\mathbf x}_n\}\) is contained in \(\Omega\), \(l_i\) are fundamental Lagrange polynomials of degree \(n\), \(N=(n+d)!/n!d!\). The article is devoted to applied questions. The authors experiment with four families of points, which are asymptotically equidistributed with respect to the Dubiner metric and estimate growth of the Lebesgue constants \(\Lambda_n(X_N)\). So called Padua points on \([-1,1]^2\) give experimental relation \(\Lambda_n=O(\log^2n)\). There are no proofs in the paper.
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 2175488
zbMATH Keywords: Lebesgue constants
zbMATH Keywords: Lagrange polynomials
MaRDI profile type: Publication
full work available at URL: j.amc.2004.07.001
OpenAlex ID: W2109990880
Wikidata QID: Q29305088
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DBLP publication ID: journals/amc/CaliariMV05
DOI: 10.1016/J.AMC.2004.07.001
description: scientific article; zbMATH DE number 2175488