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Newton's method: Sufficient conditions for practical and input-to-state stability

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Date

2020

Authors

Colabufo, Giuseppe G.
Dower, Peter M.
Shames, Iman

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Research Projects

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Abstract

Newton's method is a classical iterative algorithm for the numerical computation of isolated roots of algebraic equations and stationary points of functions. While its application is ubiquitous in a plethora of fields, questions concerning its robust stability to uncertainties in problem data and numerical accuracy often arise in practice. This paper seeks to provide sufficient conditions for practical stability, input-to-state-stability (ISS), integral ISS (iISS) and incremental ISS (δISS) of Newton's method in the presence of such uncertainties, and provide illustrative examples of their application.

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Keywords

Incremental ISS (δISS), Input-to-state stability (ISS), Integral ISS (iISS), Newton's method, Numerical methods, Robust stability

Citation

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https://hdl.handle.net/1885/733798470

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ANU Research Publications

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IFAC-PapersOnLine

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Conference paper

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Publication

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DOI

10.1016/j.ifacol.2020.12.1764

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