We establish the exact-order estimates for the best m-term approximations in the multiple Haar basis Hd of functions from the Besov classes in the Lebesgue spaces \( {L}_q\left({\mathbb{I}}^d\right) \). We also present a practical algorithm for the construction of the extreme nonlinear m-term aggregates (in a sense of the exact-order estimates for approximations).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. S. Romanyuk, “Multiple Haar basis and m-term approximations of functions from the Besov classes. I,” Ukr. Mat. Zh., 68, No. 4, 551–562 (2016).
V. S. Romanyuk, “Nonlinear approximation in spaces of multiple sequences,” in: Approximation Theory of Functions and Related Problems [in Ukrainian], Proc. of the Institute of Mathematics, Ukrainian National Academy of Sciences, 12, No. 4 (2015), pp. 256–265.
É. S. Belinskii, “Approximation by a ‘floating’ system of exponents on classes of smooth periodic functions,” Mat. Sb., 132, No. 1, 20–27 (1987).
S. A. Stasyuk, “Best m-term trigonometric approximation of periodic functions of several variables from Nikol’skii–Besov classes for small smoothness,” J. Approxim. Theory, 177, 1–16 (2014).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 68, No. 6, pp. 816–825, June, 2016.
Rights and permissions
About this article
Cite this article
Romanyuk, V.S. Multiple Haar Basis and m-Term Approximations of Functions from the Besov Classes. II. Ukr Math J 68, 928–939 (2016). https://doi.org/10.1007/s11253-016-1266-6
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-016-1266-6