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

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