Chebyshev approximations for the Fresnel integrals
Author:
W. J. Cody
Journal:
Math. Comp. 22 (1968), 450453
MathSciNet review:
0238469
Fulltext PDF Free Access
Abstract 
References 
Additional Information
Abstract: Rational Chebyshev approimations have been computed for the Fresnel integrals and for arguments in the intervals and , and for the related functions and for the intervals , and . Maximal relative errors range down to .
 [1]
Milton
Abramowitz and Irene
A. Stegun, Handbook of mathematical functions with formulas,
graphs, and mathematical tables, National Bureau of Standards Applied
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 [2]
H. E. Syrett & M. W. Wilson, Computation of Fresnel Integrals to 28 Figures: Approximations to 8 and 20 Figures, Univ. of Western Ontario, Canada. (Unpublished.) See Math. Comp., v. 20, 1966, p. 181, RMT 25.
 [3]
J.
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G.
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(32 #3265)
 [5]
W. Fraser & J. F. Hart, "On the computation of rational approximations to continuous functions," Comm. ACM, v. 5, 1962, pp. 401403.
 [6]
W. J. Cody & J. Stoer, "Rational Chebyshev approximations using interpolation," Numer. Math., v. 9, 1966, pp. 177188.
 [7]
Peter
Henrici, The quotientdifference algorithm, Nat. Bur.
Standards Appl. Math. Ser. no. 49 (1958), 23–46. MR 0094901
(20 #1410)
 [8]
John
R. Rice, On the conditioning of polynomial and rational forms,
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(32 #6710)
 [1]
 M. Abramowitz & I. A. Stegun (Editors), Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, National Bureau of Standards Appl. Math. Series, No. 55, U. S. Government Printing Office, Washington, D. C., 1964. MR 31 #1400. MR 0167642 (29:4914)
 [2]
 H. E. Syrett & M. W. Wilson, Computation of Fresnel Integrals to 28 Figures: Approximations to 8 and 20 Figures, Univ. of Western Ontario, Canada. (Unpublished.) See Math. Comp., v. 20, 1966, p. 181, RMT 25.
 [3]
 J. Boersma, "Computation of Fresnel integrals," Math. Comp., v. 14, 1960, p. 380. MR 22 #12700. MR 0121973 (22:12700)
 [4]
 G. Németh, "Chebyshev expansions for Fresnel integrals," Numer. Math., v. 7, 1965, pp. 310312. MR 32 #3265. MR 0185805 (32:3265)
 [5]
 W. Fraser & J. F. Hart, "On the computation of rational approximations to continuous functions," Comm. ACM, v. 5, 1962, pp. 401403.
 [6]
 W. J. Cody & J. Stoer, "Rational Chebyshev approximations using interpolation," Numer. Math., v. 9, 1966, pp. 177188.
 [7]
 P. Henrici, "The quotientdifference algorithm," Nat. Bur. Standards Appl. Math. Ser., no. 49, 1958, pp. 2346. MR 20 #1410. MR 0094901 (20:1410)
 [8]
 J. R. Rick, "On the conditioning of polynomial and rational forms," Numer. Math., v. 7, 1965, pp. 426435. MR 32 #6710. MR 0189283 (32:6710)
Additional Information
DOI:
http://dx.doi.org/10.1090/S0025571868998712
PII:
S 00255718(68)998712
Article copyright:
© Copyright 1968
American Mathematical Society
