Quasi-optimal convergence using interpolation by non-uniform deficient splines
by
Olivier Gilson
University of Liege
Coauthors: Omar Faure, Pascal Laubin (University of Liege)

The subject of my talk would be the approximation of regular as well as some singular functions using a particular family of splines. We consider the interpolation by deficient splines of degree 2m+1 and regularity C_m+1 on uniform but also non uniform meshes for any m >= 1. The obtained results give optimal order of convergence in Sobolev norms, even for the interpolation of fractional powers in ]0, 1[. It appears to be a useful method for the inversion of boundary integral operators where such singular functions occur.

Date received: February 12, 2001