Error bounds for Kronrod extension of generalizations of Micchelli-Rivlin quadrature formula for analytic functions

Abstract

We consider the Kronrod extension of generalizations of the Micchelli-Rivlin quadrature formula for the Fourier-Chebyshev coefficients with the highest algebraic degree of precision. For analytic functions, the remainder term of these quadrature formulas can be represented as a contour integral with a complex kernel. We study the kernel on elliptic contours with foci at the points ∓1 and the sum of semi-axes ρ>1 for the mentioned quadrature formulas. We derive L∞-error bounds and L1-error bounds for these quadrature formulas. Finally, we obtain explicit bounds by expanding the remainder term. Numerical examples that compare these error bounds are included.