Sharp asymptotics of the Lp approximation error for interpolation on block partitions

Details Sharp asymptotics of the Lp approximation error for interpolation on block partitions Sharp asymptotics of the Lp approximation error for interpolation on block partitions

2011-01-10

arxiv.org/abs/1101.1776v1

Mathematics

Numerical Analysis

20 pages, 1 figure

Scientific paper

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 IRd. 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.

Affiliated with

Also associated with

No associations

Rating

Sharp asymptotics of the Lp approximation error for interpolation on block partitions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Sharp asymptotics of the Lp approximation error for interpolation on block partitions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sharp asymptotics of the Lp approximation error for interpolation on block partitions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-456263