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Properties of Minimal Integration Rules. II

Nira Richter-Dyn
SIAM Journal on Numerical Analysis
Vol. 8, No. 3 (Sep., 1971), pp. 497-508
Stable URL: http://www.jstor.org/stable/2949668
Page Count: 12
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Properties of Minimal Integration Rules. II
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Abstract

Integration rules which minimize the norm of the error functional in Hilbert spaces of analytic functions are found to possess positive weights and points interior to the interval of integration. The results are derived by applying the theory of moment spaces of Tchebycheff systems for a class of Hilbert spaces with extended totally positive reproducing kernels, a class which is wider than the one dealt with in the previous work.

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