Geodesic
Constructive sparse trigonometric approximations of functions with small mixed smoothness
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 4, pp. 247-253

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Exact order bounds are obtained for the best $m$-term trigonometric approximation (in the integral metric) of periodic functions with small mixed smoothness from classes close to Nikol'skii-Besov type classes. The obtained bounds differ (under identical constraints on the smoothness) from the corresponding bounds of the best $m$-term trigonometric approximation of Besov classes of mixed smoothness established by A.S. Romanyuk. The upper bound is realized by a constructive method based on a greedy algorithm.
Keywords: nonlinear approximation, sparse approximation, mixed smoothness, order bounds. 
@article{TIMM_2016_22_4_a22,
     author = {S. A. Stasyuk},
     title = {Constructive sparse trigonometric approximations of functions with small mixed smoothness},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {247--253},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2016_22_4_a22/}
}
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S. A. Stasyuk. Constructive sparse trigonometric approximations of functions with small mixed smoothness. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 4, pp. 247-253. http://geodesic.mathdoc.fr/item/TIMM_2016_22_4_a22/