Quasi Interpolants and Approximation Power of Multivariate Splines.

摘要

The determination of the approximation power of spaces of multivariate splines with the aid of quasi interpolants is reviewed. In the process, streamlined description of the existing quasi interpolants theory is given. The author begins with a brief review of the approximation power of univariate splines since the techniques for its investigation are also those with which people have tried to understand the multivariate setup. (That may in fact be the reason why we know so little about it.) He then briefly discusses three examples to illustrate some basic limitations of the standard univariate approach. (KR)