This article is cited in 1 paper

Fast computation of linear combinations of Sobolev functions generated by the Haar functions

M. G. Magomed-Kasumov^ab, S. R. Magomedov<sup>a

a</sup> Daghestan Scientific Centre of Russian Academy of Sciences, Makhachkala
^b Vladikavkaz Scientific Centre of the Russian Academy of Sciences

Abstract: Some properties of orthogonal with respect to Sobolev inner product functions $\chi_{1,n}(x)$, generated by Haar functions, are considered. In particular, recurrent formulas for $\chi_{1,n}(x)$ are obtained. It is developed an algorithm for calculation of the linear combinations of $N$ functions $\chi_{1,n}(x)$ using $O(\log N)$ operations.

Keywords: Haar system, numerical method, Sobolev type inner product, fast algorithm.

UDC: 519.622

Received: 19.04.2018
Revised: 04.06.2018
Accepted: 05.06.2018

DOI: 10.31029/demr.9.2