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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The approximation order of polysplines


Authors: Ognyan Kounchev and Hermann Render
Journal: Proc. Amer. Math. Soc. 132 (2004), 455-461
MSC (2000): Primary 41A15; Secondary 35J40, 31B30
Published electronically: July 31, 2003
MathSciNet review: 2022369
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Abstract: We show that the scaling spaces defined by the polysplines of order $p$provide approximation order $2p.$ For that purpose we refine the results on one-dimensional approximation order by $L$-splines obtained by de Boor, DeVore, and Ron (1994).


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Additional Information

Ognyan Kounchev
Affiliation: Institute of Mathematics, Bulgarian Academy of Sciences, Acad. G. Bonchev St. 8, 1113 Sofia, Bulgaria
Email: kounchev@cblink.net, kounchev@math.uni-duisburg.de, kounchev@math.bas.bg

Hermann Render
Affiliation: Institute of Mathematics, University of Duisburg-Essen, Lotharstr. 65, 47048 Duisburg, Germany
Email: render@math.uni-duisburg.de

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07069-2
PII: S 0002-9939(03)07069-2
Keywords: Cardinal splines, cardinal $L$-splines, polysplines, approximation order of splines, polyharmonic functions, cardinal polysplines.
Received by editor(s): April 5, 2002
Received by editor(s) in revised form: October 2, 2002
Published electronically: July 31, 2003
Communicated by: David Sharp
Article copyright: © Copyright 2003 American Mathematical Society