On stratified extensions of Gauss-Laguerre and Gauss-Hermite quadrature formulas

Authors:
Sven Ehrich
Affiliations:
GSF-National Research Center for Environment and Health, Institute of Biomathematics and Biometrics, Ingolstadter Landstr. 1, D-85764 Neuherberg, Germany
Venue:
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Year:
2002

Citing 5
Cited 4

An overview of results on the existence or nonexistence and the error term of Gauss-Kronrod quadrature formulae

Proceedings of the conference on Approximation and computation : a fetschrift in honor of Walter Gautschi: a fetschrift in honor of Walter Gautschi
Anti-Gaussian quadrature formulas

Mathematics of Computation
Stratified nested and related quadrature rules

Journal of Computational and Applied Mathematics - Numerical evaluation of integrals
Stopping functionals for Gaussian quadrature formulas

Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. V: quadrature and orthogonal polynomials
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Modified anti-Gauss and degree optimal average formulas for Gegenbauer measure

Applied Numerical Mathematics
On numerical computation of integrals with integrands of the form f(x)sin(w/xr) on [0, 1]

Journal of Computational and Applied Mathematics
Suitable Gauss and Filon-type methods for oscillatory integrals with an algebraic singularity

Applied Numerical Mathematics
Error estimates of anti-Gaussian quadrature formulae

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

For the practical estimation of the error of Gauss-Laguerre and Gauss-Hermite quadrature formulas, it is well known that real positive Kronrod formulas do not exist. Among the alternatives which are available in the literature, the stratified rules introduced by Laurie are of particular interest. In this note, we determine the degree optimal stratified extensions for the Gauss-Laguerre and Gauss-Hermite formulas, and we investigate their properties.