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IMA Journal of Applied Mathematics 1973 12(2):159-164; doi:10.1093/imamat/12.2.159
© 1973 by Institute of Mathematics and its Applications
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A Note on Asymptotic Minimal Weights for an Integration Rule

N. S. KAMBO

Department of Mathematics, Indian Institute of Technology Hauz Khas, New Delhi—29, India

Consider an integration rule with abscissas in the interval of integration and which is exact for all polynomials up to a certain degree. The error of the rule applied to a Hilbert space of functions analytic within an ellipse containing interval of integration is a bounded linear functional. In this paper we the asymptotic weights of the rule which minimize the norm of the error functional as the underlying ellipse shrinks to the interval of integration.


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