二元矩阵有理插值函数的构造  

Method of Constructing Bivariate Matrix-valued Rational Interpolation Functions

作　　者：杜伟伟[1] 

机构地区：[1]安徽教育出版社,安徽合肥230601

出　　处：《大学数学》2011年第3期110-114,共5页College Mathematics

摘　　要：一般构造矩阵值有理函数的方法是利用连分式给出的,其算法的可行性不易预知,且计算量大.本文对于二元矩阵值有理插值的计算,通过引入多个参数,定义一对二元多项式:代数多项式和矩阵多项式,利用两多项式相等的充分必要条件通过求解线性方程组确定参数,并由此给出了矩阵值有理插值公式.该公式简单,具有广阔的应用前景.The well-known algorithms of constructing matrix-valued rational interpolations use continued fractions.Their applicability is not easily forecast and they need a large amount of calculation.In this paper,for calculation of bivariate matrix-valued rational interpolations,multi-parameters are introduced and a group of polynomials with two elements,that is an algebraic polynomial and matrix-valued polynomials,are defined.By using the necessary and sufficient conditions for polynomials identity,linear equations are solved to determine the parameters and the formula of the matrix-valued rational interpolation is given.The formula is simple,so that it has a bright application future.

关 键 词：二元矩阵值 有理插值 参数 方程组 

分 类 号：O241.3[理学—计算数学]