C-2 Tension Splines Construction Based on a Class of Sixth-Order Ordinary Differential Equations
C-2 Tension Splines Construction Based on a Class of Sixth-Order Ordinary Differential Equations
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基于一类六阶常微分方程的C-2拉伸样条构造
DOI：
10.1007/s41980-020-00505-3
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发表时间：
2022
影响因子：
0.7
通讯作者：
Han Xuli
中科院分区：
文献类型：
--
作者：
Zhu Yuanpeng;Chen Zhenbiao;Han Xuli
在这项工作中，我们基于六阶常微分方程构造了一类Hermite型插值基函数。利用它们，我们提出了一种具有局部张力参数的张力插值样条。对于插值，给定的插值具有收敛性。给出了张力插值样条在中国金融市场利率期限结构构建中的一些应用。此外，构造了$$\text {span}\left\{ {1,t, \ldots ,{t^{n - 4}},\sin (\tau t),\cos (\tau t),\sinh (\tau t),\cosh (\tau t)} \right\} $$所跨越空间的广义非均匀B样条。
In this work, we construct a class of Hermite-type interpolation basis functions based on the sixth-order ordinary differential equation. Using them, we propose a kind oftension interpolation splines with a local tension parameter. Forinterpolation, the given interpolant hasconvergence. Some applications of thetension interpolation splines on the construction of interest rate term structure in Chinese financial market are given. Moreover, a kind of generalized non-uniform B-splines of the space spanned by $$\text {span}\left\{ {1,t, \ldots ,{t^{n - 4}},\sin (\tau t),\cos (\tau t),\sinh (\tau t),\cosh (\tau t)} \right\} $$ is constructed.