## On generalized averaged Gaussian formulas

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- by Miodrag M. Spalević PDF
- Math. Comp.
**76**(2007), 1483-1492 Request permission

## 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.## References

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## Additional Information

**Miodrag M. Spalević**- Affiliation: Department of Mathematics and Informatics, University of Kragujevac, Faculty of Science, P.O. Box 60, 34000 Kragujevac, Serbia
- MR Author ID: 600543
- Email: spale@kg.ac.yu
- Received by editor(s): August 9, 2005
- Received by editor(s) in revised form: May 4, 2006
- Published electronically: March 8, 2007
- Additional Notes: The author was supported in part by the Serbian Ministry of Science and Environmental Protection (Project #144005A: “Approximation of linear operators”).
- © Copyright 2007 American Mathematical Society
- Journal: Math. Comp.
**76**(2007), 1483-1492 - MSC (2000): Primary 65D30, 65D32; Secondary 33A65
- DOI: https://doi.org/10.1090/S0025-5718-07-01975-8
- MathSciNet review: 2299784