C-2 Rational Quartic/Cubic Spline Interpolant with Shape Constraints
C-2 Rational Quartic/Cubic Spline Interpolant with Shape Constraints
复制标题
C-2 具有形状约束的有理四次/三次样条插值
DOI：
10.1007/s00025-018-0883-9
复制
发表时间：
2018
影响因子：
2.2
通讯作者：
Zhu YP
中科院分区：
文献类型：
--
作者：
Zhu Yuanpeng;Zhu YP
构造了一类具有三族局部控制参数的有理四次/三次样条插值函数，该插值函数是连续的，不需要求解整体线性或非线性的相容方程组.说明了局部控制参数对生成插值样条的影响。对于插值，给出的插值函数能局部再生二次多项式，且具有收敛性。简单的计划，建议的插值，以保持积极的，单调的，和/或凸的数据集的形状。给出了插值函数严格位于两个给定分段线性函数之间的充分条件。此外，还详细讨论了有理四次/三次插值样条的重要拐点性质。
A class of rational quartic/cubic spline interpolants with three families of local control parameters is constructed, which can becontinuous without solving a global linear or non-linear system of consistency equations. The effects of the local control parameters on generating interpolation spline are illustrated. Forinterpolation, the given interpolant can locally reproduce quadratic polynomials and hasorconvergence. Simple schemes for the proposed interpolant to preserve the shape of positive, monotonic, and/or convex set of data are derived. Sufficient conditions for the interpolant to lie strictly between two given piecewise linear functions are also given. Moreover, the important inflection property of the rational quartic/cubic interpolation spline is discussed in detail.