Tables for the Gaussian computation of for values of varying continuously between and
Authors:
P. Lambin and J. P. Vigneron
Journal:
Math. Comp. 33 (1979), 805811
MSC:
Primary 65A05
MathSciNet review:
521295
Fulltext PDF Free Access
Abstract 
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Abstract: Tables of coefficients of Chebyshev expansions for computing to 11 places the abscissas and weight factors of the 12point generalized GaussLaguerre quadrature formula are presented.
 [1]
I. S. BEREZIN & N. P. ZHIDKOV, Computing Methods, Vol. I, Pergamon Press, Oxford, 1965, p. 236.
 [2]
Z. KOPAL, Numerical Analysis, Wiley, New York, 1961.
 [3]
Arthur
Erdélyi, Wilhelm
Magnus, Fritz
Oberhettinger, and Francesco
G. Tricomi, Higher transcendental functions. Vols. I, II,
McGrawHill Book Company, Inc., New YorkTorontoLondon, 1953. Based, in
part, on notes left by Harry Bateman. MR 0058756
(15,419i)
 [4]
Herbert
E. Salzer and Ruth
Zucker, Table of the zeros and weight factors
of the first fifteen Laguerre polynomials, Bull. Amer. Math. Soc. 55 (1949), 1004–1012. MR 0032191
(11,263m), http://dx.doi.org/10.1090/S000299041949093278
 [5]
D. BURNETT, "The numerical calculation of ," Proc. Cambridge Philos. Soc., v. 33, 1937, pp. 359362.
 [6]
Philip
Rabinowitz and George
Weiss, Tables of abcissas and weights for
numerical evaluation of integrals of the form
∫₀^{∞}𝑒^{𝑥}𝑥ⁿ𝑓(𝑥)𝑑𝑥,
Math. Tables Aids Comput. 13 (1959), 285–294. MR 0107992
(21 #6713), http://dx.doi.org/10.1090/S00255718195901079923
 [7]
V. S. AIZENSHTAT, V. I. KRYLOV & A. S. METLESKII, Tables for Calculating Laplace Transforms and Integrals of the Form , Izdat. Akad. Nauk SSSR, Minsk, 1962 (Russian); reviewed in Math. Comp., v. 17, 1963, p. 93.
 [8]
P.
Concus, D.
Cassatt, G.
Jaehnig, and E.
Melby, Tables for the evaluation of
∫₀^{∞}𝑥^{𝛽}𝑒^{𝑥}𝑓(𝑥)𝑑𝑥
by GaussLaguerre quadrature, Math. Comp.
17 (1963),
245–256. MR 0158534
(28 #1757), http://dx.doi.org/10.1090/S00255718196301585349
 [9]
P. CONCUS, "Additional tables for the evaluations of by GaussLaguerre quadrature," Math. Comp., v. 18, 1964, p. 523.
 [10]
B. S. BERGER & R. DANSON, "Tables of zeros and weights for GaussLaguerre quadrature," Math. Comp., v. 22, 1968, pp. 458459.
 [11]
B. S. BERGER, R. DANSON & R. CARPENTER, "Tables of zeros and weights for GaussLaguerre quadrature to 24S for N = 400, 500 and 600, and tables of zeros and weights for GaussLaguerre quadrature to 23S for N = 700, 800 and 900," Math. Comp., v. 23, 1969, p. 882.
 [12]
V. I. KRYLOV & P. P. VOROBLEVA, Izdat. Nauka i Teknika, Minsk, 1971.
 [13]
E. N. DEKANOSIDZE, Tables of the Zeros and Weight Factors of Generalized Laguerre Polynomials, Computing Center, Acad. Sci. USSR, Moscow, 1966.
 [14]
L.
Fox and I.
B. Parker, Chebyshev polynomials in numerical analysis, Oxford
University Press, LondonNew YorkToronto, Ont., 1968. MR 0228149
(37 #3733)
 [15]
Yudell
L. Luke, Mathematical functions and their approximations,
Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New
YorkLondon, 1975. MR 0501762
(58 #19039)
 [16]
J.
H. Wilkinson, The evaluation of the zeros of illconditioned
polynomials. I, II, Numer. Math. 1 (1959),
150–180. MR 0109435
(22 #321)
 [1]
 I. S. BEREZIN & N. P. ZHIDKOV, Computing Methods, Vol. I, Pergamon Press, Oxford, 1965, p. 236.
 [2]
 Z. KOPAL, Numerical Analysis, Wiley, New York, 1961.
 [3]
 H. BATEMAN, Higher Transcendental Functions, Vol. 2, McGrawHill, New York, 1953, p. 188. MR 0058756 (15:419i)
 [4]
 H. E. SALZER & R. ZUCKER, "Tables of the zeros and weight factors of the first fifteen Laguerre polynomials," Bull. Amer. Math. Soc., v. 55, 1949, pp. 10041012. MR 0032191 (11:263m)
 [5]
 D. BURNETT, "The numerical calculation of ," Proc. Cambridge Philos. Soc., v. 33, 1937, pp. 359362.
 [6]
 P. RABINOWITZ & G. WEISS, "Tables of abscissas and weights for numerical evaluation of integrals of the form , MTAC, v. 13, 1959, pp. 285294. MR 0107992 (21:6713)
 [7]
 V. S. AIZENSHTAT, V. I. KRYLOV & A. S. METLESKII, Tables for Calculating Laplace Transforms and Integrals of the Form , Izdat. Akad. Nauk SSSR, Minsk, 1962 (Russian); reviewed in Math. Comp., v. 17, 1963, p. 93.
 [8]
 P. CONCUS, D. CASSATT, G. JACHNIG & E. MELBY, "Tables for the evaluation of by GaussLaguerre quadrature," Math. Comp., v. 17, 1963, pp. 245256. MR 0158534 (28:1757)
 [9]
 P. CONCUS, "Additional tables for the evaluations of by GaussLaguerre quadrature," Math. Comp., v. 18, 1964, p. 523.
 [10]
 B. S. BERGER & R. DANSON, "Tables of zeros and weights for GaussLaguerre quadrature," Math. Comp., v. 22, 1968, pp. 458459.
 [11]
 B. S. BERGER, R. DANSON & R. CARPENTER, "Tables of zeros and weights for GaussLaguerre quadrature to 24S for N = 400, 500 and 600, and tables of zeros and weights for GaussLaguerre quadrature to 23S for N = 700, 800 and 900," Math. Comp., v. 23, 1969, p. 882.
 [12]
 V. I. KRYLOV & P. P. VOROBLEVA, Izdat. Nauka i Teknika, Minsk, 1971.
 [13]
 E. N. DEKANOSIDZE, Tables of the Zeros and Weight Factors of Generalized Laguerre Polynomials, Computing Center, Acad. Sci. USSR, Moscow, 1966.
 [14]
 L. FOX & I. B. PARKER, Chebyshev Polynomials in Numerical Analysis, Oxford Univ. Press, London, 1968, p. 31. MR 0228149 (37:3733)
 [15]
 Y. L. LUKE, Mathematical Functions and their Approximations, Academic Press, New York, 1975, pp. 469475. MR 0501762 (58:19039)
 [16]
 J. H. WILKINSON, "The evaluation of the zeros of illconditioned polynomials, " Parts 1 and 2, Numer. Math., v. 1, 1955, pp. 150180. MR 0109435 (22:321)
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DOI:
http://dx.doi.org/10.1090/S00255718197905212957
PII:
S 00255718(1979)05212957
Article copyright:
© Copyright 1979
American Mathematical Society
