ON SPLINE INTERPOLATION FOR MONOTONE SMOOTH FUNCTION
单调光滑函数的样条插值

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.