On generalized averaged Gaussian formulas

Spalević, Miodrag

doi:10.1090/S0025-5718-07-01975-8

On generalized averaged Gaussian formulas
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by Miodrag M. Spalević PDF

Math. Comp. 76 (2007), 1483-1492 Request permission

Erratum: Math. Comp. 47 (1986), 767.

Abstract:

We present a simple numerical method for constructing the optimal (generalized) averaged Gaussian quadrature formulas which are the optimal stratified extensions of Gauss quadrature formulas. These extensions exist in many cases in which real positive Kronrod formulas do not exist. For the Jacobi weight functions $w(x)\equiv w^{(\alpha ,\beta )}(x)=(1-x)^\alpha (1+x)^\beta$ ($\alpha ,\beta >-1$) we give a necessary and sufficient condition on the parameters $\alpha$ and $\beta$ such that the optimal averaged Gaussian quadrature formulas are internal.

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