Convexity-preserving piecewise rational quartic interpolation

被引：34
|
作者：
Han, Xuli [1 ]
机构：
[1] Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410083, Peoples R China
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2008年 / 46卷 / 02期
关键词：
rational interpolation; tension spline; convexity-preserving;
D O I：
10.1137/060671577
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A family of piecewise rational quartic interpolants is given. Identified uniquely by the value of a tension parameter lambda(i), each interpolant of the family can be C(2) spline without solving a linear or nonlinear system of consistency equations for the derivative values at the knots. The interpolant can preserve the local convexity/concavity properties of the given data. A proper choice of lambda(i) to guarantee shape preservation is given. A convergence analysis establishes an error bound in terms of lambda(i) and shows that O(h(3)) accuracy is obtained for C(2) continuity. Several examples are supplied to support the practical value of the method.
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页码：920 / 929
页数：10
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