On the Lagrange and Hermite Quadrature Formula

Authors

Shuxia Li, The University of Texas Rio Grande Valley
Yonghong Chen, The University of Texas Rio Grande Valley

Document Type

Article

Publication Date

12-2024

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.

Comments

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Recommended Citation

Li, Shuxia, and Yonghong Chen. "On the Lagrange and Hermite Quadrature Formula." In Journal of Physics: Conference Series, vol. 2910, no. 1, p. 012033. IOP Publishing, 2024. http://doi.org/10.1088/1742-6596/2910/1/012033

Publication Title

Journal of Physics: Conference Series

DOI

10.1088/1742-6596/2910/1/012033