预给极点的向量连分式插值  

Vector valued continued fraction interpolation with prescribed poles

作　　者：赵前进[1] 王本强[1] ZHAO Qian jin WANG Ben - qiang(School of Science, Anhui University of Science and Technology, Huainan Anhui 232001, China)

机构地区：[1]安徽理工大学理学院,安徽淮南232001

出　　处：《安徽理工大学学报（自然科学版）》2016年第5期1-4,共4页Journal of Anhui University of Science and Technology:Natural Science

基　　金：国家自然科学基金(60973050);安徽省教育厅自然科学基金项目(KJ2009A50)

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.

关 键 词：预给极点 重数 向量有理插值 算法 

分 类 号：O241[理学—计算数学]