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Numerical Analysis and Applications

2014 year, number 4

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, pr. Lavrentieva, 6, Novosibirsk, Russia, 630090
Keywords: functional basis, elliptic operator, energy scalar product, functional, generalized solution, conjugation condition

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.