预给极点的向量连分式插值

摘要

为了保证函数在预给极点处的重数,给出了一种新算法计算预给极点的向量连分式插值.由预给的极点信息构造插值函数分母多项式的一个因式,通过每个向量值乘以一个确定的数,将预给极点的向量插值转化为无预给极点的向量插值,基于向量的Samelson逆构造Thiele型向量连分式插值,最终通过除以一个确定的函数获得预给极点的向量连分式插值.具有预给的极点且保持原有的重数.通过数值实例对比不同方法在极点附近的插值误差,说明了新方法的有效性.%In order to guarantee the number of functions in the prescribed poles , this paper presents an algorithm developed to calculate the vector valued continued fraction interpolant with prescribed poles .In the vector valued interpolant , a factorization of the denominator polynomial is constructed based on the information about the pre -scribed poles .By means of multiplying each interpolated vector value by a certain number , vector valued inter-polation with prescribed poles is transformed into the one without prescribed poles .The vector valued continued fraction interpolant is constructed based on the Samelson inverse .Finally, by dividing a defined function , the vector valued continued fraction interpolant with prescribed poles is obtained and has prescribed poles with intrin -sic multiplicity.Finally, an example is given in the text, by comparing different methods in interpolation error pole nearby , and shows the effectiveness of the new method .