QUADRATURES WITH MULTIPLE NODES FOR FOURIER-CHEBYSHEV COEFFICIENTS
2016
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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 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. 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 estimation
their error. Numerical results are included. These results are continuation of the
recent ones by Bojanov and Petrova (J. Comput. Appl. Math., 2009), and Milovanovi´c and Spalevi´c (Math. Comp., 2014).
Извор:
6th MATHEMATICAL CONFERENCE OF THE REPUBLIC OF SRPSKA, BOOK OF ABSTRACTS, 2016, 25-25Издавач:
- UNIVERSITY OF EAST SARAJEVO, MATHEMATICAL SOCIETY OF THE REPUBLIC OF SRPSKA
Институција/група
Mašinski fakultetTY - CONF AU - Milovanović, Gradimir AU - Orive, Ramon AU - Spalević, Miodrag PY - 2016 UR - https://machinery.mas.bg.ac.rs/handle/123456789/5137 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 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. 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 estimation their error. Numerical results are included. These results are continuation of the recent ones by Bojanov and Petrova (J. Comput. Appl. Math., 2009), and Milovanovi´c and Spalevi´c (Math. Comp., 2014). PB - UNIVERSITY OF EAST SARAJEVO, MATHEMATICAL SOCIETY OF THE REPUBLIC OF SRPSKA C3 - 6th MATHEMATICAL CONFERENCE OF THE REPUBLIC OF SRPSKA, BOOK OF ABSTRACTS T1 - QUADRATURES WITH MULTIPLE NODES FOR FOURIER-CHEBYSHEV COEFFICIENTS EP - 25 SP - 25 UR - https://hdl.handle.net/21.15107/rcub_machinery_5137 ER -
@conference{ author = "Milovanović, Gradimir and Orive, Ramon and Spalević, Miodrag", year = "2016", 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 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. 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 estimation their error. Numerical results are included. These results are continuation of the recent ones by Bojanov and Petrova (J. Comput. Appl. Math., 2009), and Milovanovi´c and Spalevi´c (Math. Comp., 2014).", publisher = "UNIVERSITY OF EAST SARAJEVO, MATHEMATICAL SOCIETY OF THE REPUBLIC OF SRPSKA", journal = "6th MATHEMATICAL CONFERENCE OF THE REPUBLIC OF SRPSKA, BOOK OF ABSTRACTS", title = "QUADRATURES WITH MULTIPLE NODES FOR FOURIER-CHEBYSHEV COEFFICIENTS", pages = "25-25", url = "https://hdl.handle.net/21.15107/rcub_machinery_5137" }
Milovanović, G., Orive, R.,& Spalević, M.. (2016). QUADRATURES WITH MULTIPLE NODES FOR FOURIER-CHEBYSHEV COEFFICIENTS. in 6th MATHEMATICAL CONFERENCE OF THE REPUBLIC OF SRPSKA, BOOK OF ABSTRACTS UNIVERSITY OF EAST SARAJEVO, MATHEMATICAL SOCIETY OF THE REPUBLIC OF SRPSKA., 25-25. https://hdl.handle.net/21.15107/rcub_machinery_5137
Milovanović G, Orive R, Spalević M. QUADRATURES WITH MULTIPLE NODES FOR FOURIER-CHEBYSHEV COEFFICIENTS. in 6th MATHEMATICAL CONFERENCE OF THE REPUBLIC OF SRPSKA, BOOK OF ABSTRACTS. 2016;:25-25. https://hdl.handle.net/21.15107/rcub_machinery_5137 .
Milovanović, Gradimir, Orive, Ramon, Spalević, Miodrag, "QUADRATURES WITH MULTIPLE NODES FOR FOURIER-CHEBYSHEV COEFFICIENTS" in 6th MATHEMATICAL CONFERENCE OF THE REPUBLIC OF SRPSKA, BOOK OF ABSTRACTS (2016):25-25, https://hdl.handle.net/21.15107/rcub_machinery_5137 .