﻿ 定义于椭球面上的多元Lagrange插值问题研究 Multivariate Lagrange Interpolation Defined on Ellipsoidal Surface

Vol.06 No.04(2017), Article ID:21279,6 pages
10.12677/AAM.2017.64052

Multivariate Lagrange Interpolation Defined on Ellipsoidal Surface

Tingting Hui, Haibo Liu, Lihong Cui

Liaoning Normal University, Dalian Liaoning

Received: Jun. 15th, 2017; accepted: Jul. 3rd, 2017; published: Jul. 6th, 2017

ABSTRACT

The multivariate Lagrange interpolation problem, which is usually defined on the ellipsoid, is often studied in practical scientific research and production. Multivariate Lagrange interpolation is proposed to define the definition of ellipsoid and given to determine whether the node group on an ellipsoid form judgment theorem and superposition method to construct interpolation regular set of nodes and finally is to implement the method.

Keywords:Ellipsoid, Multivariate Lagrange Interpolation, Regular Set of Nodes, Superposition Interpolation Method

1. 引言

2. 基本定义和基本定理

，令中m个互异点构成的点集，如果对于任意给定的数组，恒存在唯一多项式，使之满足：，则称的一个正则结点组。

3. 算例

Figure 1. Point of the ellipsoid

Multivariate Lagrange Interpolation Defined on Ellipsoidal Surface[J]. 应用数学进展, 2017, 06(04): 442-447. http://dx.doi.org/10.12677/AAM.2017.64052

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