A network version of the non-standard trigonometric basis and its advantages with respect to a similar polynomial basis

V. V. Smelov

Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 6 Lavrentjev pr., Novosibirsk, 630090, Russia

Abstract: A trigonometry-based functional basis as a network version is proposed. It is aimed at the approximation with high orders of accuracy of smooth and piecewise-smooth functions. A comparative analysis of the features of the basis proposed and a polynomial one is made. The trigonometric version offers considerable advantages over the polynomial bases.

Key words: functional basis, elliptic operator, energy scalar product, functional, generalized solution, conjugation condition.

UDC: 518.12+519.34

Received: 16.04.2013
Revised: 10.02.2014

 English version: Numerical Analysis and Applications, 2014, 7:4, 336–344

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