一种改进的MQ拟插值方法及其性质
A New Quasi Interpolation Scheme for MQ Radial Basis Function
DOI: 10.12677/AAM.2021.106205, PDF,    科研立项经费支持
作者: 熊 晗, 曾 光*, 王斌斌：东华理工大学理学院，江西 南昌；科学与工程计算实验室，东华理工大学理学院，江西 南昌；雷 莉*：东华理工大学理学院，江西 南昌
关键词: 数值逼近；径向基函数；拟插值；保形性；收敛阶；Numerical Approximation； Radial Basis Function； Quasi-Interpolation； Shape-Preserving； Approximation Capacity
摘要: 本文基于Wu-Schaback拟插值算子LDF(X)构造了一种新的MQ径向拟插值算子，该算子增加了在两端点处的一阶导数的线性组合项，并结合三点微分公式替代其两端点处的导数值，提高了该算子的收敛阶。通过理论分析得出该算子的线性多项式具有再生性、二阶保形性和较高的收敛阶等优点。最后，通过数值实验比较了该拟插值格式与Wu-Schaback和Feng-Li的拟插值格式的近似能力，数值计算结果证实了理论分析的正确性，验证了该算子对数值求解中的有效性。
Abstract: Based on Wu-schaback’s Quasi interpolation operator, a new MQ radial quasi interpolation operator is proposed. The operator has the advantages of linear polynomial regeneration, shape-preserving property of order 2 and high convergence rate, and does not need the derivative of the function at the end point. Through theoretical analysis, it is concluded that the linear polynomial of the operator has the advantages of reproducibility, second-order shape preservation and higher convergence order. Finally, the approximation ability of the proposed scheme is compared with Wu-scha- back’s and Feng Li’s quasi interpolation scheme by numerical experiments. The numerical results confirm the conclusion of the theoretical analysis and the effectiveness of the operator.
文章引用：熊晗, 曾光, 雷莉, 王斌斌. 一种改进的MQ拟插值方法及其性质[J]. 应用数学进展, 2021, 10(6): 1945-1955. https://doi.org/10.12677/AAM.2021.106205

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