Quadratures with multiple nodes for Fourier-Chebyshev coefficients
Само за регистроване кориснике
2019
Чланак у часопису (Објављена верзија)
Метаподаци
Приказ свих података о документуАпстракт
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).
Кључне речи:
quadratures with multiple nodes / optimal extensions / Fourier-Chebyshev coefficientsИзвор:
Ima Journal of Numerical Analysis, 2019, 39, 1, 271-296Издавач:
- Oxford Univ Press, Oxford
Финансирање / пројекти:
- Serbian Academy of Sciences and Arts [F-96]
- Spanish Ministerio de Ciencia e Innovacion [MTM2015-71352-P]
- Апроксимација интегралних и диференцијалних оператора и примене (RS-MESTD-Basic Research (BR or ON)-174015)
- Методе нумеричке и нелинеарне анализе са применама (RS-MESTD-Basic Research (BR or ON)-174002)
DOI: 10.1093/imanum/drx067
ISSN: 0272-4979
WoS: 000491255100009
Scopus: 2-s2.0-85058217081
Колекције
Институција/група
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 . .