基于导数信息的Multiquadric拟插值  

MQ Quasi-interpolation for Derivative Data

作　　者：高文武[1,2] 

机构地区：[1]安徽大学经济学院,合肥230411 [2]复旦大学数学科学学院,上海200433

出　　处：《复旦学报（自然科学版）》2016年第3期298-303,共6页Journal of Fudan University：Natural Science

基　　金：上海市现代应用数学重点实验室基金(12DZ 2272800)

摘　　要：为了使MQ拟插值能够更好地处理泛函信息的拟合问题,运用拟插值理论、数值逼近理论,研究了基于导数信息的MQ拟插值的构造理论及其性质.通过本文的研究,构造了一类基于导数信息的MQ拟插值格式并讨论了它的收敛性及保形性,为MQ拟插值在几何造型、微分方程数值解、构造动态轮廓线等领域的应用提供了理论依据.For better applications of MQ（Multiquadric） quasi-interpolation in dealing with linear functional data fitting problems, the paper studies construction and properties of MQ quasi-interpolation for derivative data with the theories of classical quasi-interpolation and numerical approximation. A quasi-interpolation scheme for derivative data is constructed in the paper. Moreover, convergence and shape preserving properties of the quasiinterpolation are also derived. The paper provides a theoretical background of MQ quasi-interpolation for applications in geometric modeling, numerical solution of differential equations, construction of active contours and so forth.

关 键 词：MQ拟插值 导数信息 保形性 收敛性 

分 类 号：O174.1[理学—数学]