Error estimates for Gauss quadrature formulas for analytic functions

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...

Error bounds for Gauss-Tur'an quadrature formulae of analytic functions

We study the kernels of the remainder term Rn,s(f) of GaussTurán quadrature formulas ∫ 1 −1 f(t)w(t) dt = n ∑

Asymptotic Error Estimates for the Gauss Quadrature Formula

Integral formulas for Chebyshev polynomials and the error term of interpolatory quadrature formulae for analytic functions

We evaluate explicitly the integrals ∫ 1 −1 πn(t)/(r ∓ t)dt, |r| = 1, with the πn being any one of the four Chebyshev polynomials of degree n. These integrals are subsequently used in order to obtain error bounds for interpolatory quadrature formulae with Chebyshev abscissae, when the function to be integrated is analytic in a domain containing [−1, 1] in its interior.

On the error term of symmetric Gauss-Lobatto quadrature formulae for analytic functions

Gauss-Lobatto quadrature formulae associated with symmetric weight functions are considered. The kernel of the remainder term for classes of analytic functions is investigated on elliptical contours. Sufficient conditions are found ensuring that the kernel attains its maximal absolute value at the intersection point of the contour with either the real or the imaginary axis. The results obtained...