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 | References | Similar Articles | Additional Information

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