TY  - JOUR
AU  - Milovanović, Gradimir V.
AU  - Orive, Ramon
AU  - Spalević, Miodrag
PY  - 2019
UR  - https://machinery.mas.bg.ac.rs/handle/123456789/3157
AB  - 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).
PB  - Oxford Univ Press, Oxford
T2  - Ima Journal of Numerical Analysis
T1  - Quadratures with multiple nodes for Fourier-Chebyshev coefficients
EP  - 296
IS  - 1
SP  - 271
VL  - 39
DO  - 10.1093/imanum/drx067
ER  - 

@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"
}

Milovanović, G. V., Orive, R.,& Spalević, M.. (2019). Quadratures with multiple nodes for Fourier-Chebyshev coefficients. in Ima Journal of Numerical Analysis
Oxford Univ Press, Oxford., 39(1), 271-296.
https://doi.org/10.1093/imanum/drx067

Milovanović GV, Orive R, Spalević M. Quadratures with multiple nodes for Fourier-Chebyshev coefficients. in Ima Journal of Numerical Analysis. 2019;39(1):271-296.
doi:10.1093/imanum/drx067 .

Milovanović, Gradimir V., Orive, Ramon, Spalević, Miodrag, "Quadratures with multiple nodes for Fourier-Chebyshev coefficients" in Ima Journal of Numerical Analysis, 39, no. 1 (2019):271-296,
https://doi.org/10.1093/imanum/drx067 . .