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关于球面上的一种Hermite插值

梁学章1, 张明2, 高占恒3, 车翔玖3   

  1. 1. 吉林大学数学研究所, 长春 130012;
    2. 东北师范大学计算机学院, 长春 130024;
    3. 吉林大学计算机科学与技术学院, 长春 130012
  • 收稿日期:2008-09-08 出版日期:2009-12-15 发布日期:2009-12-30
  • 基金资助:

    国家自然科学基金项目(60673021)和(60773098)资助

梁学章, 张明, 高占恒, 车翔玖. 关于球面上的一种Hermite插值[J]. 计算数学, 2009, 31(4): 407-418.

Liang Xuezhang, Zhang Ming, Gao Zhanheng, Che Xiangjiu. A KIND OF HERMITE INTERPOLATION ON THE SPHERE[J]. Mathematica Numerica Sinica, 2009, 31(4): 407-418.

A KIND OF HERMITE INTERPOLATION ON THE SPHERE

Liang Xuezhang1, Zhang Ming2, Gao Zhanheng3, Che Xiangjiu3   

  1. 1. Institute of Mathematics, Jilin University, Changchun 130012, China;
    2. School of Computer Science, Northest Normal University, Changchun 130024, China;
    3. College of Computer Science and Technology, Jilin University, Changchun 130012, China
  • Received:2008-09-08 Online:2009-12-15 Published:2009-12-30
本文旨在提出单位球面上的一种Hermite插值格式. 为此, 本文首先研究了沿球面同轴圆周组上的Hermite插值问题, 给出了三种适定的插值泛函组. 然后研究了球面上的Hermite插值问题, 给出了球面上Hermite插值的一种叠加插值法, 即添加圆周组法. 进一步将二者结合,导出了一类球面上Hermite插值的适定插值泛函组. 为了说明这类适定插值泛函组的构造方法,在本文最后还给出了构造球面上低次Hermite适定插值泛函组的一些具体例子和数值算例.

 

The purpose of this paper is to put forward a kind of Hermite interpolation schemes for the unit sphere surface. Firstly, we have studied Hermite interpolation on a set of coaxial circumferences along the sphere surface, and given three kinds of properly posed sets of interpolating functionals for it. Secondly, we have studied Hermite interpolation on the sphere surface, and proposed a superposition interpolation method, namely, the circumferences-superposition method. Combining these two results, we deduced a kind of properly posed set of interpolating functionals for Hermite interpolation on the sphere surface. In order to explain this method, we have given some concrete examples for structuring the properly posed set of interpolating functionals with lower degree and some numerical examples at the end of this paper.

 

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