矩阵切触有理插值函数构造方法

Constructing Methods of Matrix-Valued Osculatory Rational Interpolation Functions

矩阵切触有理插值的传统方法是连分式.连分式的优点是:格式相对固定,迭代方便;缺点是:算法的可行性是有条件的,且计算繁琐,可能出现极点或不可达点等.为了克服上述缺陷,提出了一种有别于连分式的矩阵切触有理插值的新方法.首先构造基函数及Tailor型插值算子,然后将二者作线性组合,得出各阶导数条件下的矩阵切触有理插值函数公式,证明了相应的定理,给出了误差估计及插值函数的一般计算步骤.本文的方法简单,计算量小,不需要任何附加条件,所构造的Tailor型插值算子具有承袭性,所得插值函数无极点和不可达点.数值例子说明了该方法的有效性和实用性.

The traditional method of matrix-valued osculatory rational interpolation is continued fraction,which enjoys some advantages.The former include relatively constant format and convenient iteration.The latter include conditional feasibility,complicated calculation and possibility of poles or inaccessible points.In order to overcome the disadvantages,another method of matrix-valued osculatory rational interpolation which is different from continued fraction is proposed in this paper.The primary function and the Tailor type interpolation operators are firstly constructed,which are then combined linearly to work out the formulas of matrix-valued osculatory rational interpolating function under the conditions of all order derivatives.Corresponding theorems are then proved.The error estimation and general steps of calculating interpolation functions are finally given.This method is simple with little calculation and no additional conditions.The constructed Tailor type interpolation operators are inherited.The interpolating function can be easily worked out with no poles and inaccessible points.The efficiency and practicability of the proposed method is illustrated by a numerical example.