Work

The error norm of nonsymmetric product integration rules for Chebyshev weight functions with Chebyshev abscissae

Year: 2026

Type: article

Abstract: We consider four product integration rules, two for the Chebyshev weight of the first-kind based on the Chebyshev abscissae of the third or fourth-kind, and another two for the Chebyshev weight of the second-kind based again on the Chebyshev abscissae of the third or fourth-kind. The new rules have positive weights given by explicit formulae, while the rules for the Chebyshev weight of the second-kind have the best possible degree of exactness for an interpolatory formula not of Gauss type. On certain spaces of analytic functions the error term of these rules is a continuous linear functional. By means of a new approach, we compute explicitly the norm of the error functional, which leads to efficient error bounds.

Source: BIT Numerical Mathematics

DOI: 10.1007/s10543-026-01110-2

Authors: Sotirios E. Notaris, Nikolaos J. Theodorakopoulos

Institution: National and Kapodistrian University of Athens

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: National and Kapodistrian University of Athens