Journalartikel

Jahr der Veröffentlichung: 2001

Seiten: 181-208

Zeitschrift: Constructive Approximation

Bandnummer: 17

Heftnummer: 2

ISSN: 0176-4276

DOI Link: https://doi.org/10.1007/s003650010034

Verlag: Springer

Abstract: 
Let Delta be a triangulation of some polygonal domain Omega subset of R-2 and let S-q(r)(Delta) denote the space of all bivariate polynomial splines of smoothness r and degree q with respect to Delta. We develop thr first Hermite-type interpolation scheme for S-q(r)(Delta), q greater than or equal to 3r + 2, whose approximation error is bounded above by Kh(q+1), where h is the maximal diameter of the triangles in Delta, and the constant K only depends on the smallest angle of the triangulation and is independent of near-degenerate edges and near-singular vertices. Moreover, the fundamental functions of our scheme are minimally supported and form a locally linearly independent basis for a superspline subspace of S-q(r)(Delta). This shows that the optimal approximation order can be achieved by using minimally supported splines. Our method of proof is completely different from the quasi-interpolation techniques for the study of the approximation power of bivariate splines developed in [7] and [18].

Harvard-Zitierstil: Davydov, O., Nürnberger, G. and Zeilfelder, F. (2001) Bivariate spline interpolation with optimal approximation order, Constructive Approximation, 17(2), pp. 181-208. https://doi.org/10.1007/s003650010034

APA-Zitierstil: Davydov, O., Nürnberger, G., & Zeilfelder, F. (2001). Bivariate spline interpolation with optimal approximation order. Constructive Approximation. 17(2), 181-208. https://doi.org/10.1007/s003650010034