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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

A note on extended Gaussian quadrature rules


Author: Giovanni Monegato
Journal: Math. Comp. 30 (1976), 812-817
MSC: Primary 65D30
MathSciNet review: 0440878
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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 - {\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}},{e^{ - {x^2}}}$ and $ {e^{ - x}}$. Finally, two examples are given of quadrature rules which can be extended repeatedly.


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DOI: http://dx.doi.org/10.1090/S0025-5718-1976-0440878-3
PII: S 0025-5718(1976)0440878-3
Article copyright: © Copyright 1976 American Mathematical Society