Abstract
Suppose that we are given a convergent sequence of interpolatory integration rules {I n} ∞ n=1 . What can we say about the distribution of the points in the rules? We review previous results, which show that half the points in the rules behave like zeros of appropriate orthogonal polynomials, and half may be arbitrarily distributed. In the case of the interval (-1,1), this usually means that half the points have arcsin distribution. We also present and prove a new result relating the rate at which half the points converge to the arcsin distribution, and the size of the weights in the rule I n .
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© 1993 Springer Basel AG
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Bloom, T., Lubinsky, D.S., Stahl, H.B. (1993). Distribution of Points in Convergent Sequences of Interpolatory Integration Rules: The Rates. In: Brass, H., Hämmerlin, G. (eds) Numerical Integration IV. ISNM International Series of Numerical Mathematics, vol 112. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6338-4_3
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DOI: https://doi.org/10.1007/978-3-0348-6338-4_3
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-6340-7
Online ISBN: 978-3-0348-6338-4
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