On the Lagrange and Hermite Quadrature Formula
Year: 2024
Type: conference-paper
Abstract: This paper builds on the error analysis method for Newton-Cotes quadrature formulas developed by D. R. Hayes and L. Rubin in 1970, which utilizes Lagrange interpolation polynomials. By adopting and extending their approach, this work derives the error estimate for Hermite interpolation quadrature. Specifically, we construct a polynomial P(x) analogous to the scaling function A(x) used by Hayes and Rubin, and prove its non-negativity over the interval. This allows us to establish a precise error formula for Hermite interpolation quadrature. The results provide a novel application of Hayes and Rubin’s methodology, offering new insights into error analysis for high-order interpolation quadrature formulas.
Authors: Shuxia Li, Yonghong Chen
Institution: The University of Texas Rio Grande Valley
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4405537652