Asymptotic properties of minimal integration rules

Philip Rabinowitz, Nira Richter

Research output: Contribution to journalArticlepeer-review

Abstract

The error of a particular integration rule applied to a Hubert 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.

Original languageEnglish
Pages (from-to)593-609
Number of pages17
JournalMathematics of Computation
Volume24
Issue number111
DOIs
StatePublished - Jul 1970
Externally publishedYes

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