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.
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P. CONCUS, "Additional tables for the evaluations of by GaussLaguerre quadrature," Math. Comp., v. 18, 1964, p. 523.
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B. S. BERGER & R. DANSON, "Tables of zeros and weights for GaussLaguerre quadrature," Math. Comp., v. 22, 1968, pp. 458459.
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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.
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V. I. KRYLOV & P. P. VOROBLEVA, Izdat. Nauka i Teknika, Minsk, 1971.
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E. N. DEKANOSIDZE, Tables of the Zeros and Weight Factors of Generalized Laguerre Polynomials, Computing Center, Acad. Sci. USSR, Moscow, 1966.
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L.
Fox and I.
B. Parker, Chebyshev polynomials in numerical analysis, Oxford
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 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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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197905212957
PII:
S 00255718(1979)05212957
Article copyright:
© Copyright 1979 American Mathematical Society
