A constructive approach to nodal splines

被引:7
作者
Siewer, Ralf [1 ]
机构
[1] Univ Siegen, Dept Math, D-57068 Siegen, Germany
关键词
local spline interpolation; nodal splines; polynomial reproduction;
D O I
10.1016/j.cam.2006.04.004
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In the context of local spline interpolation methods, nodal splines have been introduced as possible fundamental functions by de Villiers and Rohwer in 1988. The corresponding local spline interpolation operator possesses the desirable property of reproducing a large class of polynomials. However, it was remarked that their definition is rather intricate so that it seems desirable to reveal the actual origin of these splines. The real source can be found in the Martensenoperator which can be obtained by two-point Hermite spline interpolation problem posed and proved by Martensen [Darstellung und Entwicklung des Restgliedes der Gregoryschen Quadraturformel mit Hilfe von Spline-Funktionen, Numer. Math. 21(1973)70-80]. On the one hand, we will show how to represent the Hermite Martensen spline recursively and, on the other hand, explicitly in terms of the B-spline by using the famous Marsden identity. Having introduced the Martensenoperator, we will show that the nodal spline interpolation operator can be obtained by a special discretization of the occurring derivatives. We will consider symmetric nodal splines of odd degree that can be obtained by our methods in a natural way. (c) 2006 Published by Elsevier B.V.
引用
收藏
页码:289 / 308
页数:20
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