檀结庆,朱功勤.广义有理样条的几种构造方法[J].数学研究及应用,1995,15(4):485~498
广义有理样条的几种构造方法
A Few Constructions of Generalized Rational Splines
投稿时间:1993-09-29  
DOI:10.3770/j.issn:1000-341X.1995.04.002
中文关键词:  
英文关键词:interpolation  rational spline  Pade approximant  divided difference.
基金项目:
作者单位
檀结庆 合肥工业大学数力系 
朱功勤 合肥工业大学数力系 
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中文摘要:
      本文利用Thiele倒差分方法、Pade逼近方法、广义Q.D.算法及ε-算法等构造了几种广义有理样条函数.此外,通过直接法构造了(k-1,k)-型广义有理样条,给出了它的行列式表示和余项表示并证明了广义有理样条算子的存在性、唯一性、齐次性及连续性.
英文摘要:
      The aim of this paper is to construct a few kinds of generalized interpolatingrational splines by various method, including Thiele’s reciprocal difference method, Padeapproximant method, generalized Q.D.algorithm and generalized ε-algorithm. Amongothers we also establish in direct way the determinant representations and remainderrepresentations of the generalized rational splines of type (k - 1, k) and prove some prop-erties of them,such as existence, uniqueness, homogeneity and continuity of generalized rational spline operators.
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