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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

   

 

Two-stage approximation methods with extended B-splines


Authors: O. Davydov, J. Prasiswa and U. Reif
Journal: Math. Comp. 83 (2014), 809-833
MSC (2010): Primary 41A15; Secondary 65D07
Published electronically: July 10, 2013
MathSciNet review: 3143693
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Abstract: We develop and analyze a framework for two-stage methods with EB-splines, applicable to continuous and discrete approximation problems. In particular, we propose a weighted discrete least squares fit that yields optimal convergence rates for sufficiently dense data on Lipschitz domains in $ \mathbb{R}^d$.


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Additional Information

O. Davydov
Affiliation: Department of Mathematics, University of Strathcylde, 26 Richmond Street, Glasgow, G1 1XH United Kingdom
Email: oleg.davydov@strath.ac.uk

J. Prasiswa
Affiliation: Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt, Germany
Email: praiswa@mathematik.tu-darmstadt.de

U. Reif
Affiliation: Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt, Germany
Email: reif@mathematik.tu-darmstadt.de

DOI: http://dx.doi.org/10.1090/S0025-5718-2013-02734-2
Received by editor(s): December 17, 2010
Received by editor(s) in revised form: June 1, 2012
Published electronically: July 10, 2013
Additional Notes: The first author was supported in part by a Research Fellowship from the Alexander von Humboldt Foundation.
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.