APPROXIMATION ORDER OF BIVARIATE SPLINE INTERPOLATION

Authors
Citation
G. Nurnberger, APPROXIMATION ORDER OF BIVARIATE SPLINE INTERPOLATION, Journal of approximation theory, 87(2), 1996, pp. 117-136
Citations number
17
Categorie Soggetti
Mathematics, Pure",Mathematics
ISSN journal
00219045
Volume
87
Issue
2
Year of publication
1996
Pages
117 - 136
Database
ISI
SICI code
0021-9045(1996)87:2<117:AOOBSI>2.0.ZU;2-T
Abstract
In [G. Nurnberger and Th. Riessinger, numer. Math. 71 (1995), 91-119], we developed an algorithm for constructing point sets at which unique Lagrange interpolation by spaces of bivariate splines of arbitrary de gree and ssmoothness, on uniform type triangulations is possible. Here , we show that similar Hermite interpolation sets field (nearly) optim al approximation order. This is shown for differentiable splines of de gree at least four defined on non-rectangular domains subdivided in un iform type triangles. Therefore. in practice we use Lagrange configura tions which are ''close'' to these Hermite configurations. Application s to data fitting problems and numerical examples are given. (C) 1996 Academic Press, Inc.