Near minimally normed spline quasi-interpolants on uniform partitions (Q557732)

Spline quasi-interpolants (QIs) are local approximating operators for functions or discrete data. The authors construct discrete and integral spline QIs on uniform partition of the real line with optimal approximation orders and small norms by minimizing a simple upper bound of the true norm. These can be used to approximate functions with isolated discontinuities. It is observed that this method gives good results with respect to the infinity norm but the constant appearing in the standard estimation of the quasi-interpolation error is too crude. A study of nonuniform partition and bi-variate cases are projected as future work of the authors which are communicated for publication.