An analog to Gaussian quadrature implemented on a specific trigonometric basis

V. V. Smelov, A. S. Popov

Institute of Computational Mathematics and Mathematical Geophysics (Computing Center), Siberian Branch of the Russian Academy of Sciences, Novosibirsk

Abstract: A new quadrature formula based on a nonstandard basis of trigonometric functions is constructed. The quadrature is comparable in accuracy to the Gauss quadrature formula and is used with the same class of functions. However, this quadrature has nothing to do with the quadrature for periodic functions, which is also based on trigonometric functions.

Key words: quadrature formula, weight function, nodes and coefficients of a quadrature, approximation.

UDC: 519.644

Received: 10.11.2009
Revised: 27.11.2009

 English version: Numerical Analysis and Applications, 2010, 3:4, 357–366

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