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Error Estimates for Gauss-Laguerre and Gauss-Hermite Quadrature Formulas

  • G. Mastroianni
  • G. Monegato
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 119)

Abstract

New error estimates are derived for Gauss-Laguerre and Gauss-Hermite m—point quadrature formulas; they are of the type \(O\,({m^{ - r/2}})\,\left\| {{x^{r/2}}} \right.{f^{(r)}}\left. {{x^\alpha }{e^{ - x}}} \right\|\,{L_1}\) and \(O\,({m^{ - r/2}})\,\left\| {{f^{(r)}}} \right.\left. {{e^{ - qx2}}} \right\|{L_1},\,0 <\,q\,1\) respectively, for functions f in suitable function classes.

Keywords

Orthogonal Polynomial Quadrature Formula Remainder Term Infinite Interval Geometric Convergence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser 1994

Authors and Affiliations

  • G. Mastroianni
    • 1
  • G. Monegato
    • 2
  1. 1.Dipartimento di MatematicaUniversità della BasilicataItalia
  2. 2.Dipartimento di MatematicaPolitecnico di TorinoItalia

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