Quadrature formulas for Fourier coefficients

Borislav Bojanov; Guergana Petrova

doi:10.1016/j.cam.2009.02.097

Quadrature formulas for Fourier coefficients

Borislav Bojanov, Guergana Petrova

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives. © 2009 Elsevier B.V. All rights reserved.

Original language	English (US)
Pages (from-to)	378-391
Number of pages	14
Journal	Journal of Computational and Applied Mathematics
Volume	231
Issue number	1
DOIs	https://doi.org/10.1016/j.cam.2009.02.097
State	Published - Sep 2009
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: The first author was supported by the Sofia University Research grant # 135/2008 and by Swiss-NSF Scopes Project IB7320-111079. The work of second author has been supported in part by the NSF Grants #DMS-0505501 and #DMS-0810869, and by Award # KUS-C1-016-04, given by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.1016/j.cam.2009.02.097

Cite this

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author = "Borislav Bojanov and Guergana Petrova",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-C1-016-04 Acknowledgements: The first author was supported by the Sofia University Research grant # 135/2008 and by Swiss-NSF Scopes Project IB7320-111079. The work of second author has been supported in part by the NSF Grants #DMS-0505501 and #DMS-0810869, and by Award # KUS-C1-016-04, given by King Abdullah University of Science and Technology (KAUST). This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

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AB - We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives. © 2009 Elsevier B.V. All rights reserved.

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JF - Journal of Computational and Applied Mathematics

IS - 1

ER -

Quadrature formulas for Fourier coefficients

Abstract

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