A note on extended Gaussian quadrature rules

Monegato, Giovanni

doi:10.1090/S0025-5718-1976-0440878-3

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.

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