Monotonicity of the error term in Gauss-Turán quadratures for analytic function

Abstract

For Gauss-Turan quadrature formulae with an even weight function on the interval [-1, 1] and functions analytic in regions of the complex plane which contain in their interiors a circle of radius greater than 1, the error term is investigated. In some particular cases we prove that the error decreases monotonically to zero. Also, for certain more general cases, we illustrate how to check numerically if this property holds. Some £ 2 -error estimates are considered.2000 Mathematics subject classification: primary 41A55; secondary 65D30, 65D32.

Quadrature with multiple nodes, power orthogonality, and moment-preserving spline approximation, part II

“…Indeed, they can be chosen to snuggle tightly around the interval [−1, 1] by selecting ρ sufficiently close to 1, thereby avoiding possible singularities or excessive growth of f . The circular contours are used in [56] and [60].…”

Ocene gresaka kvadraturnih formula Gausovog tipa za analiticke funkcije

“…} , (n, β/α, δ/α) ρ * , ρ min (n, β/α, δ/α) ρ * , ρ min (n, β/α, δ/α) ρ * , ρ min (10, 2.1, 1.07) 1.583, 1.581 (10,50,45) 1.888, 1.879 (10, 500, 400) 3.077, 3.075 (100, 2.1, 1.07) 1.582, 1.582 (100, 50,45) 1.880, 1.879 (100, 500, 400) 3.077, 3.075 (10, 2.1, 1.09) 1.375, 1.099 (10,50,48) 1.582, 1.325 (10,…”