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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 | References | Similar Articles | Additional Information

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

Hermann Render
Affiliation: Institute of Mathematics, University of Duisburg-Essen, Lotharstr. 65, 47048 Duisburg, Germany

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