广义有理样条的几种构造方法

A Few Constructions of Generalized Rational Splines

本文利用Ｔｈｉｅｌｅ倒差分方法、Ｐａｄｅ逼近方法、广义Ｑ．Ｄ．算法及ε－算法等构造了几种广义有理样条函数．此外，通过直接法构造了（ｋ－１，ｋ）－型广义有理样条，给出了它的行列式表示和余项表示并证明了广义有理样条算子的存在性、唯一性、齐次性及连续性．

The aim of this paper is to construct a few kinds of generalized interpolatingrational splines by various method, including Thiele’s reciprocal difference method, Padeapproximant method, generalized Q.D.algorithm and generalized ε-algorithm. Amongothers we also establish in direct way the determinant representations and remainderrepresentations of the generalized rational splines of type (k - 1, k) and prove some prop-erties of them,such as existence, uniqueness, homogeneity and continuity of generalizedrational spline operators.