关于广义逆的向量连分式插值样条

本文首次引入了关于广义逆的向量有理插值样条的概念．这类插值样条具有Thiele型连分式的截断分式的表现形式．在它的构造过程中，不必用到连分式的三项递推关系，本文得到的新的有效的系数算法具有递推运算的特点．存在性的一个充分条件得以建立．包括唯一性在内的有关插值问题的某些结果得到证明．最后，本文给出了一个精确的插值误差公式．

On Generalized Inverse Vector Valued Continued Fraction Interpolation Splines

The definition of vector valned continned fraction interpolating splines is at first introduced by means of generalized inverse of a vector. In the computation of the interpolating splines,which are of representation of the convergences for Thiele-type continned fraction.the three relation is avioded and a new effective recursive algorithm is constrncted. A sufficient condition for existence is given. Some interpolation results incluing uniqueness are given. In the end. a exact interpolation remainder formula is obtained.