## A note on extended Gaussian quadrature rules

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- by Giovanni Monegato PDF
- Math. Comp.
**30**(1976), 812-817 Request permission

## Abstract:

Extended Gaussian quadrature rules of the type first considered by Kronrod are examined. For a general nonnegative weight function, simple formulas for the computation of the weights are given, together with a condition for the positivity of the weights associated with the new nodes. Examples of nonexistence of these rules are exhibited for the weight functions $(1-x^2)^{\lambda - 1/2}$, $e^{-x^2}$ and $e^{-x}$. Finally, two examples are given of quadrature rules which can be extended repeatedly.## References

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## Additional Information

- © Copyright 1976 American Mathematical Society
- Journal: Math. Comp.
**30**(1976), 812-817 - MSC: Primary 65D30
- DOI: https://doi.org/10.1090/S0025-5718-1976-0440878-3
- MathSciNet review: 0440878