Unisolvency for multivariate polynomial interpolation in Coatmèlec configurations of nodes

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• 作者：Miguel Á ; ngel Garc&#xed ; a-March^a ; Fernando Gim&#xe9 ; nez^b ; Francisco R. Villatoro^c ; Jezabel P&#xe9 ; rez^b ; ^{jperezq@mat.upv.es} ; Pedro Fern&#xe1 ; ndez de Có ; rdoba^b
• 关键词：Multivariate interpolation ; Properly posed set of nodes ; Geometric characterization ; Coatm&#xe8 ; lec lattices
• 刊名：Applied Mathematics and Computation
• 出版年：2011
• 出版时间：15 May 2011
• 年：2011
• 卷：217
• 期：18
• 页码：7427-7431
• 全文大小：165 K

文摘

A new and straightforward proof of the unisolvability of the problem of multivariate polynomial interpolation based on Coatmèlec configurations of nodes, a class of properly posed set of nodes defined by hyperplanes, is presented. The proof generalizes a previous one for the bivariate case and is based on a recursive reduction of the problem to simpler ones following the so-called Radon–Bézout process.