Quadrature formulas of the highest trigonometric accuracy grade and their applications (Q941257)

In this interesting paper the author studies approximative and structural properties of quadrature formulas of the highest trigonometric accuracy grade. He obtains the following conclusion: the well-known classical quadrature formulas obtained by Hermite and Gauss with the Chebyshev weight of the second kind, as well as the Clenshaw-Curtis formula [cf. \textit{C. W. Clenshaw} and \textit{A. R. Curtis}, Numer. Math. 2, 197--205 (1960; Zbl 0093.14006)] represent special cases of a quadrature formula of the highest trigonometric accuracy grade under a proper choice of its parameters. The second part of the paper is dedicated to the application of these formulas in numerical analysis of Fredholm integral equations with periodic coefficients.