Abstract. How to get a shape preserving approximating curve for non-parametric data has been discussed not very much in the literature, because this problem is more complicate than that for parametric data. On the other hand, the problem is raised often in applications. Conti and others have addressed the problem by using quasi-interpolation with quadric B-splines. We will generalize their discussions: we use a linear combination of the data to build a quasi-interpolation, and prove that the quasi-interpolation possesses a better approximation order and some properties of shape preserving.

Keywords: quasi-interpolation, order of approximation, shape preserving, B-spline, polynomial reproducing.

This work is supported by NSFC 19971017 and NOYG 10125102.