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Mathematics of Computation

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Asymptotic properties of minimal integration rules


Authors: Philip Rabinowitz and Nira Richter-Dyn
Journal: Math. Comp. 24 (1970), 593-609
MSC: Primary 65D30
DOI: https://doi.org/10.1090/S0025-5718-1970-0298946-X
MathSciNet review: 0298946
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Abstract: The error of a particular integration rule applied to a Hilbert space of functions analytic within an ellipse containing the interval of integration is a bounded linear functional. Its norm, which depends on the size of the ellipse, has proved useful in estimating the truncation error occurring when the integral of a particular analytic function is approximated using the rule in question. It is thus of interest to study rules which minimize this norm, namely minimal integration rules. The present paper deals with asymptotic properties of such minimal integration rules as the underlying ellipses shrink to the interval of integration.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1970-0298946-X
Keywords: Hilbert space of analytic functions, norm of error functional, minimizing abscissae and weights, minimal norm integration rule, complete orthonormal set, asymptotic properties of minimal rules
Article copyright: © Copyright 1970 American Mathematical Society