We estimate the error of Gauss-Jacobi quadrature rule applied to a function f, which is supposed locally absolutely continuous in some Besov type spaces, or of bounded variation on [-1,1]. In the first case the error bound concerns the weighted main part phi-modulus of smoothness of f introduced by Z. Ditzian and V. Totik, while in the second case we deal with a Stieltjes integral with respect to f. The stated estimates generalize several error bounds from literature and, in both the cases, they assure the same convergence rate of the error of best polynomial approximation in weighted L-1 space. (C) 2017 IMACS. Published by Elsevier B.V. All rights reserved.
Some error bounds for Gauss-Jacobi quadrature rules
Themistoclakis;Woula
2017
Abstract
We estimate the error of Gauss-Jacobi quadrature rule applied to a function f, which is supposed locally absolutely continuous in some Besov type spaces, or of bounded variation on [-1,1]. In the first case the error bound concerns the weighted main part phi-modulus of smoothness of f introduced by Z. Ditzian and V. Totik, while in the second case we deal with a Stieltjes integral with respect to f. The stated estimates generalize several error bounds from literature and, in both the cases, they assure the same convergence rate of the error of best polynomial approximation in weighted L-1 space. (C) 2017 IMACS. Published by Elsevier B.V. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.