An iterated quasi-interpolation approach for derivative approximation
An iterated quasi-interpolation approach for derivative approximation
复制标题
一种求导数近似的迭代准插值方法
DOI：
10.1007/s11075-019-00812-9
复制
发表时间：
2020
影响因子：
2.1
通讯作者：
Wenwu Gao
中科院分区：
文献类型：
--
作者：
Zhengjie Sun;Zongmin Wu;Wenwu Gao
给定在均匀中心采样的离散函数值，用于逼近 th 导数的迭代准插值方法由两个步骤组成。第一步采用算子DQ的连续应用（先是准插值算子Q，然后是微分算子D）来得到均匀中心处的三阶导数的近似值。然后，通过将准插值算子 Q 进一步应用到相应的近似导数值，给出了 3 阶导数的最终近似值。该方法最显着的特点是它以相同的收敛速度逼近所有导数。此外，与迄今为止仅对周期函数有效的现有迭代插值方法相比，它对一般多元函数有效。本文最后给出了基于B样条准插值和多重二次准插值的迭代和直接方法逼近高阶导数的数值例子，表明迭代准插值方法比相应的直接方法提供了更高的逼近阶数。
Given discrete function values sampled at uniform centers, the iterated quasi-interpolation approach for approximating themth derivative consists of two steps. The first step adoptsmsuccessive applications of the operator DQ (the quasi-interpolation operatorQfirst, and then the differentiation operatorD) to get approximated values of themth derivative at uniform centers. Then, by one further application of the quasi-interpolation operatorQto corresponding approximated derivative values gives the final approximation of themth derivative. The most salient feature of the approach is that it approximates all derivatives with the same convergence rate. In addition, it is valid for a general multivariate function, compared with the existing iterated interpolation approaches that are only valid for periodic functions, so far. Numerical examples of approximating high-order derivatives using both the iterated and direct approach based on B-spline quasi-interpolation and multiquadric quasi-interpolation are presented at the end of the paper, which demonstrate that the iterated quasi-interpolation approach provides higher approximation orders than the corresponding direct approach.