Lagrange基函数的复矩阵有理插值及连分式插值

1引言 矩阵有理插值问题与系统线性理论中的模型简化问题和部分实现问题有着紧密的联系~1]2]，在矩阵外推方法中也常常涉及线性或有理矩阵插值问题~3]。按照文~1]的阐述。目前已经研究的矩阵有理插值问题包括矩阵幂级数和Newton-Pade逼近。Hade逼近，联立Pade逼近，M-Pade逼近，多点Pade逼近等。显然，上述各种形式的矩阵Pade逼上梁山近是矩

COMPLEX MATRIX VALUED RATIONAL INTERPOLATION FOR LAGRANGE BASIC FUNCTIONS AND CONTINUED FRACTION INTERPOLATION

The matrix rational interpolation is very useful in the partial realization problem and model reduction for the linear system theory l].2]. In this paper. the complex matrix valued rational interpolation problem with distinct interpolation points is discussed in the frist place. Based on Lagrange basic function, the matrix rational interpolating functions are constructed in the form : a determinantal formula for denominator polynomials and a Lagrange formula for numerator matrix polynomials. Some different type examples, which include real and complex interpolation points, real and complex interpolated matrices, are given. The connection between Lagrange type rational interpolants in this paper and continued fraction type rational interpolants 4] is proposed by an example.