Weighted cubic and biharmonic splines
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- 作者：Boris Kvasov ; Tae-Wan Kim
- 关键词：monotone and convex interpolation ; weighted cubic and biharmonic splines ; adaptive choice of shape control parameters ; differential multipoint boundary value problem ; successive overrelaxation method ; finite ; difference schemes in fractional steps
- 刊名：Computational Mathematics and Mathematical Physics
- 出版年：2017
- 出版时间：January 2017
- 年：2017
- 卷：57
- 期：1
- 页码：26-44
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Computational Mathematics and Numerical Analysis;
- 出版者：Pleiades Publishing
- ISSN：1555-6662
- 卷排序：57
文摘
In this paper we discuss the design of algorithms for interpolating discrete data by using weighted cubic and biharmonic splines in such a way that the monotonicity and convexity of the data are preserved. We formulate the problem as a differential multipoint boundary value problem and consider its finite-difference approximation. Two algorithms for automatic selection of shape control parameters (weights) are presented. For weighted biharmonic splines the resulting system of linear equations can be efficiently solved by combining Gaussian elimination with successive over-relaxation method or finite-difference schemes in fractional steps. We consider basic computational aspects and illustrate main features of this original approach.