【摘要】 <正> ELI Passow在[1]中提出了X={x_i}(x_i-1<x_i,-∞<i<∞)上的单调样条插值问题,并给出该问题在S（2,X）中有解的一个充分条件（记号S（m,X）表示以X为节点的m次样条函数空间）.类似的问题以前也有不少人讨论过. 本文讨论有限区间上的单调光滑函数插值问题,简称问题M.更多还原

【Abstract】 In this paper, we obtain a necessary and sufficient condition for the existence ofmonotone cubic Spline interpolant. For the monotone smooth function, we suggest ageneral interpolation, i.e., establishing the cubic pseudo-Hermite interpolant and beingmatched with the technique of smoothing piecewise linear function with integration.Finally the error bound for the given interpolation is estimated. The error bound withO(h~3) holds.更多还原