Computations with half-range Chebyshev polynomials

Authors:
Bojan Orel;Andrej Perne
Affiliations:
University of Ljubljana, Faculty of Computer and Information Science, Traška cesta 25, 1000 Ljubljana, Slovenija;University of Ljubljana, Faculty of Electrical Engineering, Traška cesta 25, 1000 Ljubljana, Slovenija
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

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Abstract

An efficient construction of two non-classical families of orthogonal polynomials is presented in the paper. The so-called half-range Chebyshev polynomials of the first and second kinds were first introduced by Huybrechs in Huybrechs (2010) [5]. Some properties of these polynomials are also shown. Every integrable function can be represented as an infinite series of sines and cosines of these polynomials, the so-called half-range Chebyshev-Fourier (HCF) series. The second part of the paper is devoted to the efficient computation of derivatives and multiplication of the truncated HCF series, where two matrices are constructed for this purpose: the differentiation and the multiplication matrix.