High accuracy B-spline quasi-interpolants and applications in numerical analysis
High accuracy B-spline quasi-interpolants and applications in numerical analysis
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DOI：
10.1080/00036811.2021.2016718
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发表时间：
2021-12
影响因子：
1.1
通讯作者：
Shenggang Zhang;C. Zhu;Qinjiao Gao
中科院分区：
文献类型：
--
作者：
Shenggang Zhang;C. Zhu;Qinjiao Gao
本文利用多结点高阶展开和精确A-离散方法，对经典的三次B-样条拟插值进行了修正。提出的四次样条拟插值具有较高的精度，计算量增加较小，同时不需要目标函数的额外信息。应用所提出的拟插值，我们开发了高精度的求积公式和微分矩阵。所有相应的误差估计与显式系数。数值实验表明了拟插值的有效性。
In this paper, we modify the classical cubic B-spline quasi-interpolant by utilizing multi-node higher-order expansions and the -exact A-discretization approach. The proposed quartic spline quasi-interpolant possesses higher accuracy with small computational complexity increased, while requires no additional information of the target function. Applying the proposed quasi-interpolant, we develop high accuracy quadrature formulas and the differentiation matrices. All corresponding error estimates with explicit coefficients are provided. Numerical experiments illustrate the effectiveness of the proposed quasi-interpolants.