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An algorithm for Filon quadrature

Authors:

Stephen M. Chase,

Lloyd D. FosdickAuthors Info & Claims

Communications of the ACM, Volume 12, Issue 8

Pages 453 - 457

https://doi.org/10.1145/363196.363209

Published: 01 August 1969 Publication History

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Abstract

An algorithm for Filon quadrature is described. Considerable attention has been devoted to an analysis of the round-off and truncation errors. The algorithm includes an automatic error control feature.

References

[1]

TEIJELO, LINDA. Algorithm 255. Comm. ACM 8, 5 (May 1965), 279.

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[2]

FILON, L. N. G. On a quadrature formula for trigonometric integrals. Proc. Roy. Soc. Edinburgh 49 (1928-29), 38.

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[3]

HAMMING, R.W. Numerical Methods for Scientists and Engineers. McGraw-Hill, New York, 1962, p. 319.

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[4]

FOSDICK, LLOYD D. Math. Comput. 2P (1968), 77.

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[5]

DAVIS, PHILIP J. Interpolation and Approximation. Blaisdell, Waltham, Mass., 1965.

Google Scholar

[6]

LUKE, YUDELL L. On the computation of oscillatory integrals. Proc. Cambridge Philos. Soc. 50 (1954), 269.

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[7]

CHASE, STEPHEN M. AND FOSDICK, LLOYD D. Algorithm 353- Filon Quadrature. Comm. ACM 12, 8 (Aug. 1969), 457-458.

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https://doi.org/10.1016/j.trgeo.2021.100696
Uetrecht J(2018)A Clamped Simpson's RuleThe College Mathematics Journal10.1080/07468342.1988.1197308919:1(43-52)Online publication date: 30-Jan-2018
https://doi.org/10.1080/07468342.1988.11973089
Gariazzo SMena ORamírez HBoubekeur L(2017)Primordial power spectrum features in phenomenological descriptions of inflationPhysics of the Dark Universe10.1016/j.dark.2017.07.00317(38-45)Online publication date: Sep-2017
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Index Terms

An algorithm for Filon quadrature
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Numerical differentiation
    2. Quadrature

Recommendations

Algorithm 353: Filon quadrature [D1]
Algorithm 418: calculation of Fourier integrals [D1]

The most commonly used formula for calculating Fourier integrals is Filon's formula, which is based on the approximation of the function by a quadratic in each double interval. In order to obtain a better approximation the cubic spline fit is used in [1]...
Remark on algorithm 353 [D1]: Filon quadrature

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Published In

Communications of the ACM Volume 12, Issue 8

Aug. 1969

59 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/363196

Editor:
M. Stuart Lynn
IBM Scientific Center, Houston, TX

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Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 August 1969

Published in CACM Volume 12, Issue 8

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Lamprea-Pineda AConnolly DHussein M(2022)Beams on elastic foundations – A review of railway applications and solutionsTransportation Geotechnics10.1016/j.trgeo.2021.10069633(100696)Online publication date: Mar-2022
https://doi.org/10.1016/j.trgeo.2021.100696
Uetrecht J(2018)A Clamped Simpson's RuleThe College Mathematics Journal10.1080/07468342.1988.1197308919:1(43-52)Online publication date: 30-Jan-2018
https://doi.org/10.1080/07468342.1988.11973089
Gariazzo SMena ORamírez HBoubekeur L(2017)Primordial power spectrum features in phenomenological descriptions of inflationPhysics of the Dark Universe10.1016/j.dark.2017.07.00317(38-45)Online publication date: Sep-2017
https://doi.org/10.1016/j.dark.2017.07.003
Shampine L(2013)Efficient Filon method for oscillatory integralsApplied Mathematics and Computation10.1016/j.amc.2013.06.085221(691-702)Online publication date: 1-Sep-2013
https://dl.acm.org/doi/10.1016/j.amc.2013.06.085
Eftimiu CHuddleston P(2012)Scattering of electromagnetic waves by conducting periodic surfaces: A comparison of exact integral equation methodsRadio Science10.1029/RS022i005p0081522:5(815-824)Online publication date: 7-Dec-2012
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Lefeuve-Mesgouez GMesgouez AChiavassa GLombard B(2012)Semi-analytical and numerical methods for computing transient waves in 2D acoustic/poroelastic stratified mediaWave Motion10.1016/j.wavemoti.2012.04.00649:7(667-680)Online publication date: Nov-2012
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El Ayadi APicoux BLefeuve-Mesgouez GMesgouez APetit C(2012)An improved dynamic model for the study of a flexible pavementAdvances in Engineering Software10.1016/j.advengsoft.2011.05.03844:1(44-53)Online publication date: 1-Feb-2012
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Shampine L(2011)Integrating oscillatory functions in MatlabInternational Journal of Computer Mathematics10.1080/00207160.2010.53733088:11(2348-2358)Online publication date: 1-Jul-2011
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Kythe PSchäferkotter M(2010)BibliographyHandbook of Computational Methods for Integration10.1201/9780203490303.bmatt(551-583)Online publication date: 15-Jan-2010
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Abstract

References

Cited By

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Recommendations

Algorithm 353: Filon quadrature [D1]

Algorithm 418: calculation of Fourier integrals [D1]

Remark on algorithm 353 [D1]: Filon quadrature

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