B-spline quasi-interpolation sampling representation and sampling recovery in Sobolev spaces of mixed smoothness

Dinh Dũng

B-spline quasi-interpolation sampling representation and sampling recovery in Sobolev spaces of mixed smoothness

Numerical Analysis 2016-11-29 v4

Authors: Dinh Dũng

Abstract

We proved direct and inverse theorems on B-spline quasi-interpolation sampling representation with a Littlewood-Paley-type norm equivalence in Sobolev spaces $W^r_p$ of mixed smoothness $r$ , established estimates of the approximation error of recovery in $L_q$ -norm of functions from the unit ball $U^r_p$ in the spaces $W^r_p$ by linear sampling algorithms based on this representation, the asymptotic optimality of these sampling algorithms in terms of Smolyak sampling width $r^s_n(U^r_p, L_q)$ and sampling width $r_n(U^r_p, L_q)$ .

Keywords

b-spline quasi-interpolation sampling representation sampling recovery Sobolev spaces of mixed smoothness linear sampling algorithms approximation error Smolyak sampling width

Cite

@article{arxiv.1603.01937,
  title  = {B-spline quasi-interpolation sampling representation and sampling recovery in Sobolev spaces of mixed smoothness},
  author = {Dinh Dũng},
  journal= {arXiv preprint arXiv:1603.01937},
  year   = {2016}
}

Comments

arXiv admin note: text overlap with arXiv:1502.01447

B-spline quasi-interpolation sampling representation and sampling recovery in Sobolev spaces of mixed smoothness

Abstract

Keywords

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