A family of Gauss-Kronrod quadrature formulae
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- by Walter Gautschi and Theodore J. Rivlin PDF
- Math. Comp. 51 (1988), 749-754 Request permission
Abstract:
We show, for each $n \geq 1$, that the $(2n + 1)$-point Kronrod extension of the n-point Gaussian quadrature formula for the measure \[ d{\sigma _\gamma }(t) = {(1 + \gamma )^2}{(1 - {t^2})^{1/2}}dt/({(1 + \gamma )^2} - 4\gamma {t^2}),\quad - 1 < \gamma \leq 1,\] has the properties that its $n + 1$ Kronrod nodes interlace with the n Gauss nodes and all its $2n + 1$ weights are positive. We also produce explicit formulae for the weights.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Math. Comp. 51 (1988), 749-754
- MSC: Primary 65D32
- DOI: https://doi.org/10.1090/S0025-5718-1988-0958640-X
- MathSciNet review: 958640