Research On Spline's Exactness

Spline's exactness is firstly mentioned in [31]by Schoenberg in 1946. By using the basic mathematical tool of harmonic analysis, he established several special splines with certain degree, continunity, exactness and span in that paper. In this thesis, we further investigate the relationship between the spline'exactness and its span, and construct a special spline with minimal span when its exactness reach the maximum. Then, we consider how to describe the above problem with multivariate mathematical tool when we extend the univariate case to multivariate one so that we can continuously investigate certain multivariate box splines with their exactness and span.