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 -