Conference Proceedings

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

Giuseppe G Colabufo, Peter M Dower, Iman Shames

IFAC PAPERSONLINE | ELSEVIER | Published : 2020

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.

Grants

Awarded by Australian Government


Funding Acknowledgements

Partially supported by the US Air Force Office of Scientific Research and the Australian Government, through grants FA2386-16-1-4066 and AUSMURIB000001/ONR MURI N00014-19-1-2571.