@article{
author = "Milovanović, Gradimir V. and Orive, Ramon and Spalević, Miodrag",
year = "2019",
abstract = "Gaussian quadrature formulas, relative to the Chebyshev weight functions, with multiple nodes and their optimal extensions for computing the Fourier coefficients in expansions of functions with respect to a given system of orthogonal polynomials, are considered. The existence and uniqueness of such quadratures is proved. One of them is a generalization of the well-known Micchelli-Rivlin quadrature formula. The others are new. A numerically stable construction of these quadratures is proposed. By determining the absolute value of the difference between these Gaussian quadratures with multiple nodes for the Fourier-Chebyshev coefficients and their corresponding optimal extensions, we get the well-known methods for estimating their error. Numerical results are included. These results are a continuation of the recent ones in Bojanov & Petrova (2009, J. Comput. Appl. Math., 231, 378-391) and Milovanovic & Spalevic (2014, Math. Comput., 83, 1207-1231).",
publisher = "Oxford Univ Press, Oxford",
journal = "Ima Journal of Numerical Analysis",
title = "Quadratures with multiple nodes for Fourier-Chebyshev coefficients",
pages = "296-271",
number = "1",
volume = "39",
doi = "10.1093/imanum/drx067"
}