Discrete Cubic Interpolatory Splines

Abstract

In the present paper, existence, uniqueness and convergence properties of a discrete cubic spline which satisfies certain averaging interpolatory condition are established. This type of interpolatory condition has been studies earlier for usual cubic splines in [3]. More precise range for weights involved in the interpolatory condition and sharper error estimates than in [3], are obtained in the present paper. © 1992, Research Institute forMathematical Sciences. All rights reserved.