Quadratures with multiple nodes for Fourier-Chebyshev coefficients
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).
Keywords:
quadratures with multiple nodes / optimal extensions / Fourier-Chebyshev coefficientsSource:
Ima Journal of Numerical Analysis, 2019, 39, 1, 271-296Publisher:
- Oxford Univ Press, Oxford
Funding / projects:
- Serbian Academy of Sciences and Arts [F-96]
- Spanish Ministerio de Ciencia e Innovacion [MTM2015-71352-P]
- Approximation of integral and differential operators and applications (RS-MESTD-Basic Research (BR or ON)-174015)
- Methods of Numerical and Nonlinear Analysis with Applications (RS-MESTD-Basic Research (BR or ON)-174002)
DOI: 10.1093/imanum/drx067
ISSN: 0272-4979
WoS: 000491255100009
Scopus: 2-s2.0-85058217081
Collections
Institution/Community
Mašinski fakultetTY - 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 . .