Department

Mathematics

Document Type

Article

Publication Date

3-2011

Abstract

Adaptive approximation (or interpolation) takes into account local variations in the behavior of the given function, adjusts the approximant depending on it, and hence yields the smaller error of approximation. The question of constructing optimal approximating spline for each function proved to be very hard. In fact, no polynomial time algorithm of adaptive spline approximation can be designed and no exact formula for the optimal error of approximation can be given. Therefore, the next natural question would be to study the asymptotic behavior of the error and construct asymptotically optimal sequences of partitions. In this paper we provide sharp asymptotic estimates for the error of interpolation by splines on block partitions in \mathbbRdRd . We consider various projection operators to define the interpolant and provide the analysis of the exact constant in the asymptotics as well as its explicit form in certain cases.

Journal

Numerische Mathematik

Journal ISSN

0029-599X

Volume

117

Issue

3

First Page

397

Last Page

423

Digital Object Identifier (DOI)

10.1007/s00211-010-0355-y

Comments

The final publication is available at Springer via http://dx.doi.org/10.1007/s00211-010-0355-y

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