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Algorithm 331: Gaussian quadrature formulas

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Walter GautschiAuthors Info & Claims

Communications of the ACM, Volume 11, Issue 6

Pages 432 - 436

https://doi.org/10.1145/363347.363392

Published: 01 June 1968 Publication History

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References

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CHANDRASEKHAR, S. Radiative Transfer. Oxford U. Press, New York, 1950, Ch. 2.

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CONY, W. J. Chebyshev approximations for the complete elliptic integrals K and E. Math. Comput. 19 (1965), 105-112.

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GAUTSCHI, W. AND CAHILL, W. F. Exponential integral and related functions. In Handbook of Mathematical Functions (M. Abramowitz and I. A. Stegun, Eds.), NBS Appl. Math. Ser. 55, 1964, U.S. Govt. Printing Office, Washington D.C., Ch. 5.

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GAUTCHL W. Construction of Gauss-Christoffel quadrature formulas. Math. Comput. 22 (1968), 251-270.

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KRYLOV, V. I., AND PAL'CEV, A.A. Approximate integration of functions having logarithmic singularities. (Russian) Vesci Akad. Navuk BSSR, Ser. Fiz.-Teh. Navuk (1962), No. 1, 13-18.

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STROUD, A. H., AND SECREST, DON. Gaussian Quadrature Formulas. Prentice-Hall, Englewood Cliffs, N. J., 1966.

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Zhang XZhang YZhang JYang PZhu J(2019)Single-shot curvature sensing with non-coaxial Fibonacci-sieve filter in telescopeApplied Physics Letters10.1063/1.5128426115:23Online publication date: 2-Dec-2019
https://doi.org/10.1063/1.5128426
Gautschi W(2015)Polynomials orthogonal with respect to exponential integralsNumerical Algorithms10.1007/s11075-014-9943-870:1(215-226)Online publication date: 1-Sep-2015
https://dl.acm.org/doi/10.1007/s11075-014-9943-8
Holden GFreeman D(2011) Monte Carlo Investigation of the Thermodynamic Properties of (H 2 O) n and (H 2 O) n H 2 ( n = 2−20) Clusters The Journal of Physical Chemistry B10.1021/jp201082p115:16(4725-4744)Online publication date: 4-Apr-2011
https://doi.org/10.1021/jp201082p
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Remark on algorithm 331: Gaussian quadrature formulas [D1]
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Special issue: Proceedings of the conference on orthogonal functions and related topics held in honor of Olav Njåstad

In this paper we consider polynomials orthogonal with respect to an oscillatory weight function w(x)=xe^i^m^@p^x on [-1,1], where m is an integer. The existence of such polynomials as well as several of their properties (three-term recurrence relation, ...

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Communications of the ACM Volume 11, Issue 6

June 1968

130 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/363347

Editor:
Gerard Salton
Cornell Univ., Ithaca, NY

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Association for Computing Machinery

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Publication History

Published: 01 June 1968

Published in CACM Volume 11, Issue 6

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Zhang XZhang YZhang JYang PZhu J(2019)Single-shot curvature sensing with non-coaxial Fibonacci-sieve filter in telescopeApplied Physics Letters10.1063/1.5128426115:23Online publication date: 2-Dec-2019
https://doi.org/10.1063/1.5128426
Gautschi W(2015)Polynomials orthogonal with respect to exponential integralsNumerical Algorithms10.1007/s11075-014-9943-870:1(215-226)Online publication date: 1-Sep-2015
https://dl.acm.org/doi/10.1007/s11075-014-9943-8
Holden GFreeman D(2011) Monte Carlo Investigation of the Thermodynamic Properties of (H 2 O) n and (H 2 O) n H 2 ( n = 2−20) Clusters The Journal of Physical Chemistry B10.1021/jp201082p115:16(4725-4744)Online publication date: 4-Apr-2011
https://doi.org/10.1021/jp201082p
Lombardi G(2009)Design of quadrature rules for Müntz and Müntz‐logarithmic polynomials using monomial transformationInternational Journal for Numerical Methods in Engineering10.1002/nme.268480:13(1687-1717)Online publication date: 31-Jul-2009
https://doi.org/10.1002/nme.2684
Freeman DDoll J(2007)The Quantum Mechanics of ClustersAdvances in Chemical Physics10.1002/9780470122693.ch4(139-179)Online publication date: 14-Mar-2007
https://doi.org/10.1002/9780470122693.ch4
Garcia R(1999)The application of nonclassical orthogonal polynomials in particle transport theoryProgress in Nuclear Energy10.1016/S0149-1970(99)00018-935:3-4(249-273)Online publication date: Jan-1999
https://doi.org/10.1016/S0149-1970(99)00018-9
Stenger F(1994)Numerical Methods via TransformationsApproximation and Computation: A Festschrift in Honor of Walter Gautschi10.1007/978-1-4684-7415-2_36(543-550)Online publication date: 1994
https://doi.org/10.1007/978-1-4684-7415-2_36
Ehrich S(1993)On the Construction of Gaussian Quadrature Formulae containing Preassigned NodesNumerical Integration IV10.1007/978-3-0348-6338-4_6(67-76)Online publication date: 1993
https://doi.org/10.1007/978-3-0348-6338-4_6
Freeman DDoll J(1985)Quantum Monte Carlo study of the thermodynamic properties of argon clusters: The homogeneous nucleation of argon in argon vapor and ‘‘magic number’’ distributions in argon vaporThe Journal of Chemical Physics10.1063/1.44876882:1(462-471)Online publication date: Jan-1985
https://doi.org/10.1063/1.448768
Gragg WHarrod W(1984)The numerically stable reconstruction of Jacobi matrices from spectral dataNumerische Mathematik10.1007/BF0140556544:3(317-335)Online publication date: 1-Oct-1984
https://dl.acm.org/doi/10.1007/BF01405565
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Remark on algorithm 331: Gaussian quadrature formulas [D1]

Remark on Algorithm 331: Gaussian quadrature formulas

Orthogonal polynomials and Gaussian quadrature rules related to oscillatory weight functions

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