Error Estimates for a Chebyshev Quadrature Method

Chebyshev series method for computing weighted quadrature formulas

In this paper we study convergence and computation of interpolatory quadrature formulas with respect to a wide variety of weight functions. The main goal is to evaluate accurately a definite integral, whose mass is highly concentrated near some points. The numerical implementation of this approach is based on the calculation of Chebyshev series and some integration formulas which are exact for ...

Error Estimates for Gauss Quadrature Formulas for Analytic Functions

1. Introduction. The estimation of quadrature errors for analytic functions has been considered by Davis and Rabinowitz [1]. An estimate for the error of the Gaussian quadrature formula for analytic functions was obtained by Davis [2]. McNamee [3] has also discussed the estimation of error of the Gauss-Legendre quadrature for analytic functions. Convergence of the Gaussian quadratures was discu...

Almost - Interpolatory Chebyshev Quadrature

The requirement that a Chebyshev quadrature formula have distinct real nodes is not always compatible with the requirement that the degree of precision of an npoint formula be at least equal to n. This condition may be expressed as | \d\ \p = 0, 1 g p, where d (dx, ■ ■ ■ , d„) with Mo(w) ~ , -IT dj = 2w A iM ; = 1, 2, • • ■ , z!, ZJ ,_, Pj(io), j = 0, 1, • • • , are the moments of the weight fu...

Asymptotic Error Estimates for the Gauss Quadrature Formula

Error Estimates for Nitsche’s Method

1.