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有理插值的广义QD算法

徐国良   

  1. 中国科学院计算中心
  • 出版日期:1988-02-20 发布日期:1988-02-20

徐国良. 有理插值的广义QD算法[J]. 数值计算与计算机应用, 1988, 9(2): 72-85.

A GENERALIZATION OF THE QD ALGORITHM FOR RATIONAL HERMITE INTERPOLATION

  1. Xu Guo-liang Computing Center, Academia Sinica
  • Online:1988-02-20 Published:1988-02-20
在Pade表的研究与计算中,Rutishauser的QD算法起着重要作用。该算法可用于构造Pade表中的一个下降阶梯上的元素,即若级数f(z)=sum from i=0 to ∞(c_iz~i)正规(对于所有m和n,Hankel矩阵H(m,n,n)非奇异,那么对于任何k≥1,存在连分式 。_b。0。。b。n0。。b。 f_k(z)=c_0+c_1z+…+c_(k-1)z~(k-1)+((c_kz~k)/1)-((q_1~kz)/1)-((e_1~kz)/1)-((q_2~kz)/1)-((e_2~kz)/1)-…,
In this paper a generalization of Rutishauer's QD algorithm for Pade approximation tothat for rational Hermite interpolation is given. A generalized QD table is thus obtained. Onits basis, we establish various three-term recurrence formulas for the elements of the cationalHermite interpolation table and continued fraction expressions for those on different "paths".As its application, we also discuss the computation of zeros or poles for meromorphic func-tions.
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