Computations with half-range Chebyshev polynomials

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摘要

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.

论文关键词:Half-range Chebyshev polynomials,Orthogonal polynomials,Three term recurrence relation,Differentiation matrix,Multiplication matrix

论文评审过程:Received 13 April 2011, Revised 11 October 2011, Available online 20 October 2011.

论文官网地址:https://doi.org/10.1016/j.cam.2011.10.006