关于三次插值样条函数的局部性质

近年来,三次插值样条函数的局部性质,受到了人们的注意,翁祖荫考察了在一般边界条件下三次插值样条的局部逼近性质及插值样条导数的局部界值,不过他对于分

ON THE LOCAL PROPERTY OF CUBIC INTERPOLATION SPLINE

This article investigates the property of cubic interpolation spline under the ge-neral end conditions. In the case of that the local mesh ratio is less than [3+5~(1/2)]/2we obtain the local bounds of the derivative of the cubic interpolation spline, andwe have proved that when a function is locally continuous and the mesh length lo-cally converges to zero, the local convergence property of its cubic interpolationspline still holds.