ERROR ANALYSIS IN INTERPOLATION BY BIVARIATE C-1-SPLINES

In two recent papers by Nurnberger & Riessinger algorithms were develo ped for constructing point sets at which unique Lagrange interpolation by spaces of bivariate splines of arbitrary-degree and smoothness on uniform-type triangulations is possible. Furthermore in Numberger (199 6 J. Approx. Theory 87, 117-136) we proved that similar Hermite interp olation sets yield (nearly) optimal approximation order. This was done for differentiable splines of degree at least four defined on domains divided into subrectangles with one diagonal. In this paper, we analy ze the error of Hermite interpolation by differentiable splines of arb itrary degree, where to each subrectangle of the partition two diagona ls are added, and show that this method yields (nearly) optimal approx imation order. The method of proof is different from that used in Nurn berger (1996). Finally, numerical examples and applications to data fi tting are given.