• 论文 • 上一篇    下一篇

一个三次样条插值定理

张宝琳   

  1. 北京应用物理与计算数学研究所
  • 出版日期:1984-03-14 发布日期:1984-03-14

张宝琳. 一个三次样条插值定理[J]. 计算数学, 1984, 6(3): 317-318.

A THEOREM ON CUBIC SPLINE INTERPOLATION

  1. Zhang Bao-lin Institute of Applied Physics and Computational Mathematics
  • Online:1984-03-14 Published:1984-03-14
C.Davis和W.J.Kammerer曾先后用不同的方法证明了如下定理: 设y_0,y_1,…,y_n为实数,满足y_0>y_1,y_1y_3,…,则存在唯一的一个n次多项式P_n(x)和一组点x_0,x_1,…,x_n使得P_n(x_i)=y_i(i=0,1,…,n),P′_n(x_i)=0(i=1,2,…,n-1),0=x_0
The following result is given to extend a theorem established by C. Davis and W J.Kammerer: If y_0, y_1, …, y_n are real numbers satisfying y_0>y_1, y_1y_3, …, then thereexists a unique cubic spline S(x)∈C~2 [0, 1] and a set of its knots x_0, x_1, …, x_n such thatS(x_i)=y_i, i=0, 1, …. n,S(x_i)=0, i=0, 1, …, n,0=x_0
()

[1] C. Davis, Extrema of a polynomial, Amer. Math. Monthly, 64 (1957) , 679-680.
[2] W. J. Kammerer, Polynomial approximation to finitely oscillating function, Math. Comput., 15(1961) , 115-119.
[3] R. S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, N. J., 1962.
No related articles found!
阅读次数
全文


摘要