多元矩阵值切触有理插值

Multivariate Matrix Valued Osculatory Rational Interpolation

将矩阵值切触有理插值问题转化为求R-模的Groebner基问题,并用递推算法计算模的Groebner基.利用这个Groebner基,可以得到包含多元矩阵值有理插值问题所有可能弱解(P(X),q(X))的参数化形式.针对具体应用,可以通过选择恰当的参数获取所需的矩阵值有理插值解.

The task of seeking the weak solution （P（X）,q（X）） of matrix valued osculatory rational interpolation was converted into computing the Groebner bases of R-submodule M of the free module over the polynomial ring. This Groebner bases can be computed recursively to obtain a parametric rational interpolation function with the Groebner bases. Choosing these parameters properly,we may get the desired matrix valued rational interpolation function.