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 Title
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