TY - JOUR

T1 - Asymptotic properties of minimal integration rules

AU - Rabinowitz, Philip

AU - Richter, Nira

PY - 1970/7

Y1 - 1970/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84968480769&partnerID=8YFLogxK

U2 - 10.1090/S0025-5718-1970-0298946-X

DO - 10.1090/S0025-5718-1970-0298946-X

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AN - SCOPUS:84968480769

SN - 0025-5718

VL - 24

SP - 593

EP - 609

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 111

ER -