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单调及保凸二次样条插值

张宝琳   

  1. 应用物理与计算数学研究所
  • 出版日期:1983-04-14 发布日期:1983-04-14

张宝琳. 单调及保凸二次样条插值[J]. 计算数学, 1983, 5(4): 367-371.

MONOTONE AND CONVEX QUADRATIC SPLINE INTERPOLATION

  1. Zhang Bao-lin Institute of Applied Physics and Computational Mathematics
  • Online:1983-04-14 Published:1983-04-14
本文将集中研究保形二次样条插值.假设序列X={x_i}和Y={y_i}(i=0,1,2,…,N)满足x_(i-1)
In this paper the necessary and sufficient condition for the existence of monotone qua-tratic interpolating spline is obtained, and then the problem proposed and studied by E.Passow is solved. A necessary and sufficient condition for the existence of monotone andconvex quadratic interpolatory spline is also established, and it is proved that such a condi-tion is equivalent to the one on 1/1 -algorithm given by F. McAllister, E. Passow and J. A.Roulier.
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[1] E. Passow, Monotone guadratic spline interpolation, J. Approximation Theory 19(1977) , 143--147.
[2] 文涛,单调光滑函数的保凸插值方法,计算数学,2:4(1980) ,299-306.
[3] E. Passow, J. A. Roulier, Monotone and convex spline interpolation, SIAM J. Numer. Anal., 14(1977) , 904-905.
[4] D. F. McAllister, E. Passow, J. A. Roulier, Algrithms of computing shape preserving spline interpolations to data, Math. Comput., 31(1977) , 717--725.
[5] D. F. McAllister, J. A, Roulier, Interpolation by convex guadratic splines, Math. Comput., 32(1978) , 1154--1162.
[6] 张宝琳,二次插值样条函数及其收敛性质,1978年全国数值代数会议交流文献.
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