Birkhoff polynomial interpolation with applications to differential equations

Kelly, Ryan Joseph (2023) Birkhoff polynomial interpolation with applications to differential equations. Masters thesis, Northern Arizona University.

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Abstract

An error formula for Birkhoff interpolation of functions on R^s is developed. Some applications of the error formula to Birkhoff quadrature methods and finite difference methods are presented. In one dimension, the formula is used to find optimal placements of interpolation nodes that maximize the local rate of convergence of the interpolating polynomial to the interpolated function. An application of Birkhoff interpolation in approximating solutions of first order initial value problems is noted.

Item Type:	Thesis (Masters)
Publisher’s Statement:	© Copyright is held by the author. Digital access to this material is made possible by the Cline Library, Northern Arizona University. Further transmission, reproduction or presentation of protected items is prohibited except with permission of the author.
Keywords:	Birkhoff quadlature; Polynomial interpolation; Differential equations; Finite difference methods
Subjects:	Q Science > QA Mathematics
NAU Depositing Author Academic Status:	Student
Department/Unit:	Graduate College > Theses and Dissertations College of the Environment, Forestry, and Natural Sciences > Mathematics and Statistics
Date Deposited:	15 May 2025 21:43
Last Modified:	15 May 2025 21:43
URI:	https://openknowledge.nau.edu/id/eprint/6138

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