On stable local bases for bivariate polynomial spline spaces

Authors
Davydov, O Schumaker, LL
Citation
O. Davydov et Ll. Schumaker, On stable local bases for bivariate polynomial spline spaces, CONSTR APPR, 18(1), 2002, pp. 87-116
Citations number
31
Categorie Soggetti
Mathematics
Journal title
CONSTRUCTIVE APPROXIMATION
ISSN journal
01764276 → ACNP
Volume
18
Issue
1
Year of publication
2002
Pages
87 - 116
Database
ISI
SICI code
0176-4276(2002)18:1<87:OSLBFB>2.0.ZU;2-J
Abstract
Stable locally supported bases are constructed for the spaces S-d(r)(Delta) of polynomial splines of degree d greater than or equal to 3r + 2 and smoo thness r defined on triangulations A, as well as for various superspline su bspaces. In addition, we show that for r greater than or equal to 1, in gen eral, it is impossible to construct bases which are simultaneously stable a nd locally linearly independent.