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research article
Approximation Properties Of Sobolev Splines And The Construction Of Compactly Supported Equivalents
In this paper, we construct compactly supported radial basis functions that satisfy optimal approximation properties. Error estimates are determined by relating these basis functions to the class of Sobolev splines. Furthermore, we derive new rates for approximation by linear combinations of nonuniform translates of the Sobolev splines. Our results extend previous work as we obtain rates for basis functions of noninteger order, and we address approximation with respect to the L-infinity norm. We also use bandlimited approximation to determine rates for target functions with lower order smoothness.
Type
research article
Web of Science ID
WOS:000338830800006
Authors
Publication date
2014
Publisher
Published in
Volume
46
Issue
3
Start page
1843
End page
1858
Peer reviewed
REVIEWED
EPFL units
Available on Infoscience
August 29, 2014
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