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Chebyshev-type quadrature for analytic weights on the circle and the interval

By A.B.J. Kuijlaars

Abstract

AbstractWe give a sharp asymptotic bound on the number of nodes needed for Chebyshev-type (= equal weight) quadrature of degree p for measures on [−1, 1] of the form w(t)(π√ 1 − t2)dt, where w is positive on [−1, 1] and analytic in a neighborhood of [−1, 1]. This bound is derived from a corresponding bound for Chebyshev-type quadrature for analytic weights on the unit circle. In addition, we present some results on Chebyshev-type quadrature on certain algebraic curves

Publisher: Published by Elsevier B.V.
Year: 1995
DOI identifier: 10.1016/0019-3577(96)81757-5
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