Polar forms and quadratic spline quasi-interpolants on Powell–Sabin partitions

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• 作者：D. Sbibih ; A. Serghini ; A. Tijini
• 关键词：Polar forms ; Quasi-interpolation ; Quadratic splines ; Powell– ; Sabin partitions
• 刊名：Applied Numerical Mathematics
• 出版年：2009
• 出版时间：May 2009
• 年：2009
• 卷：59
• 期：5
• 页码：938-958
• 全文大小：1219 K

文摘

In this paper we introduce the Powell–Sabin B-spline representation of quadratic polynomials or splines in terms of their polar forms. We use this B-representation for constructing several differential or discrete quasi-interpolants which have an optimal approximation order. This new approach is simple and provides an efficient tool for describing many schemes of approximation involving values and (or) derivatives of a given function.