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.


Published in:
Siam Journal On Mathematical Analysis, 46, 3, 1843-1858
Year:
2014
Publisher:
Philadelphia, Siam Publications
ISSN:
0036-1410
Keywords:
Laboratories:




 Record created 2014-08-29, last modified 2018-11-14

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