• 论文 •

### 单调及保凸二次样条插值

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

### 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

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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