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Nonexistence of extended Gauss-Laguerre and Gauss-Hermite quadrature rules with positive weights

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Abstract

A simple necessary condition on the nodes is used to establish that extended Gauss-Laguerre and Gauss-Hermite quadrature formulas (Kronrod type) do not exist with positive weights whenn>0 in the Laguerre case andn=3 orn>4 in the Hermite case.

Zusammenfassung

Mit Hilfe einer einfachen notwendigen Bedingung für die Knoten wird gezeigt, daß keine erweiterten Gauß-Laguerre- bzw. Gauß-Hermite-Quadraturformeln (vom Kronrod-Typ) mit positiven Gewichten existieren, wenn im Falle der ersterenn>0, im Falle der letzterenn=3 odern>4 gilt.

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Bibliography

  1. A. Ralston,A First Course in Numerical Analysis, McGraw-Hill, New York (1965).

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  2. A. S. Kronrod,Nodes and Weights of Quadrature formulas, Consultants Bureau, New York (1965).

    Google Scholar 

  3. G. Monegato,A Note of Extended Gaussian Quadrature Rules, Math. Comp.30, 812–817 (1976).

    Google Scholar 

  4. G. Monegato,Positivity of the Weights of Extended Gauss-Legendre Quadrature Rules, Math. Comp.32, 243–245 (1978).

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  5. G. Szegö,Über gewisse orthogonale Polynome, die zu einer oszillierenden Bewegungsfunktion gehören, Math. Ann.110, 501–513 (1934).

    Google Scholar 

  6. G. Szegö,Orthogonal Polynomials, Amer. Math. Soc. Coll. Publ.23, New York (1975).

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Authors and Affiliations

  1. Los Alamos Scientific Lab., University of California, Los Alamos, New Mexico, USA

    D. K. Kahaner

  2. Istituto di Calcoli Numerici, Universita di Torino, Torino, Italy

    G. Monegato

Authors
  1. D. K. Kahaner
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  2. G. Monegato
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Additional information

Work supported by DOE contract #W-7405-ENG. 36, the Italian Research Concil and ETH-Zürich, Forschungs-institut für Mathematik.

Supported by the Italian Research Council.

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Kahaner, D.K., Monegato, G. Nonexistence of extended Gauss-Laguerre and Gauss-Hermite quadrature rules with positive weights. Journal of Applied Mathematics and Physics (ZAMP) 29, 983–986 (1978). https://doi.org/10.1007/BF01590820

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  • DOI: https://doi.org/10.1007/BF01590820

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