CAJ | 학술논문

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.
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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.