Approximation theory

Daghestan Electronic Mathematical Reports, Issue 9 (2018)

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

Magomed-Kasumov Magomedrasul Grozbekovich, Magomedov Salikh Rasulovich

UDK: 519.622

Pages: 7 - 14

DOI: 10.31029/demr.9.2


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.




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