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 rho > 1 for the mentioned quadrature formulas. We derive L-infinity-error bounds and L-1-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.