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Certification of Algorithm 363 [S15]: Complex Error Function

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K. S. KölbigAuthors Info & Claims

Communications of the ACM, Volume 15, Issue 6

Pages 465 - 466

https://doi.org/10.1145/361405.361425

Published: 01 June 1972 Publication History

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References

[1]

Gautschi, W. Error function and Fresnel integrals. Chap. 7 in Handbook of Mathematical Functions, M. Abramowitz and J.A. Stegun, Eds. NBS Appl. Math, Ser. 55, U.S. Govt. Printing Office, Washington, D.C., 1965.

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Cody, W.J. Rational Chebyshev approximations for the error function. Math. Comp. 22 (1968), 631-637.

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Bulirsch, R. Numerical calculation of the sine, cosine and Fresnel integrals, Handbook Series Special Functions. Numer. Math. 9 (1967), 380--385.

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Cody, W.J., Paciorek, K.A., andThacher, H.C.Jr. Chebyshev approximations for Dawson's integral. Math. Comp. 24 (1970), 171-178.

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Pollard RCardile CLewis DBrown L(2018)Characterization of FeOOH polymorphs and ferrihydrite using low-temperature, applied-field, Mössbauer spectroscopyClay Minerals10.1180/claymin.1992.027.1.0627:1(57-71)Online publication date: 9-Jul-2018
https://doi.org/10.1180/claymin.1992.027.1.06
Schreier F(2011)Optimized implementations of rational approximations for the Voigt and complex error functionJournal of Quantitative Spectroscopy and Radiative Transfer10.1016/j.jqsrt.2010.12.010112:6(1010-1025)Online publication date: Apr-2011
https://doi.org/10.1016/j.jqsrt.2010.12.010
Faussurier G(2004)Description of strongly coupled Yukawa fluids using the variational modified hypernetted chain approachPhysical Review E10.1103/PhysRevE.69.06640269:6Online publication date: 2-Jun-2004
https://doi.org/10.1103/PhysRevE.69.066402
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Algorithm 363: complex error function [S15]
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This paper presents a method for efficient Radial basis function (RBF) evaluation if compactly supported radial basis functions (CSRBF) are used. Application of CSRBF leads to sparse matrices, due to limited influence of radial basis functions in ...

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Communications of the ACM Volume 15, Issue 6

June 1972

69 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/361405

Editor:
M. Stuart Lynn
Rice Univ., 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

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Published: 01 June 1972

Published in CACM Volume 15, Issue 6

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Pollard RCardile CLewis DBrown L(2018)Characterization of FeOOH polymorphs and ferrihydrite using low-temperature, applied-field, Mössbauer spectroscopyClay Minerals10.1180/claymin.1992.027.1.0627:1(57-71)Online publication date: 9-Jul-2018
https://doi.org/10.1180/claymin.1992.027.1.06
Schreier F(2011)Optimized implementations of rational approximations for the Voigt and complex error functionJournal of Quantitative Spectroscopy and Radiative Transfer10.1016/j.jqsrt.2010.12.010112:6(1010-1025)Online publication date: Apr-2011
https://doi.org/10.1016/j.jqsrt.2010.12.010
Faussurier G(2004)Description of strongly coupled Yukawa fluids using the variational modified hypernetted chain approachPhysical Review E10.1103/PhysRevE.69.06640269:6Online publication date: 2-Jun-2004
https://doi.org/10.1103/PhysRevE.69.066402
Burgt PEck JHeideman H(1999)Orbital angular momentum exchange in post-collision interactionJournal of Physics B: Atomic and Molecular Physics10.1088/0022-3700/18/5/01918:5(999-1009)Online publication date: 1-Jan-1999
https://doi.org/10.1088/0022-3700/18/5/019
Herren CDousse J(1997) Experimental evidence for the - radiative Auger effect in medium-mass atoms Physical Review A10.1103/PhysRevA.56.275056:4(2750-2758)Online publication date: 1-Oct-1997
https://doi.org/10.1103/PhysRevA.56.2750
Herren CDousse J(1996) High-resolution measurements of the K - MM radiative Auger effect in medium-mass atoms Physical Review A10.1103/PhysRevA.53.71753:2(717-725)Online publication date: 1-Feb-1996
https://doi.org/10.1103/PhysRevA.53.717
Dana VMandin JAllout MRégalia L(1996)Variation of the experimental conditions during the recording in FTS: Effects on the determination of line intensities and collisional widthsJournal of Quantitative Spectroscopy and Radiative Transfer10.1016/0022-4073(96)00015-556:1(119-131)Online publication date: Jul-1996
https://doi.org/10.1016/0022-4073(96)00015-5
Galley GDousse J(1994) Forbidden - radiative atomic transition Physical Review A10.1103/PhysRevA.50.305850:4(3058-3064)Online publication date: 1-Oct-1994
https://doi.org/10.1103/PhysRevA.50.3058
Hamdouni ABarbe APlateaux JLanglois VDana VMandin JBadaoui M(1993)Measurements of N2-induced shifts and broadening coefficients of lines in CO fundamental from Fourier transform spectraJournal of Quantitative Spectroscopy and Radiative Transfer10.1016/0022-4073(93)90075-S50:3(247-255)Online publication date: Sep-1993
https://doi.org/10.1016/0022-4073(93)90075-S
Marwick ALiu JZabel TDoyle J(1992)Use of simulations of 15N profiling in studying hydrogen segregation at interfacesNuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms10.1016/0168-583X(92)95505-L64:1-4(408-412)Online publication date: Feb-1992
https://doi.org/10.1016/0168-583X(92)95505-L
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Algorithm 363: complex error function [S15]

Algorithm 421: complex gamma function with error control [S14]

Efficient Speed-Up of Radial Basis Functions Approximation and Interpolation Formula Evaluation

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