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

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

doi:10.1016/j.ifacol.2020.12.1764

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

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

^*Corresponding author for this work

Research output: Contribution to journal › Conference article › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	6334-6339
Number of pages	6
Journal	IFAC-PapersOnLine
Volume	53
Issue number	2
DOIs	https://doi.org/10.1016/j.ifacol.2020.12.1764
Publication status	Published - 2020
Externally published	Yes
Event	21st IFAC World Congress 2020 - Berlin, Germany Duration: 12 Jul 2020 → 17 Jul 2020

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@article{cc45011b77b1426180b7bdf20be64a20,

title = "Newton's method: Sufficient conditions for practical and input-to-state stability",

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.",

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

author = "Colabufo, {Giuseppe G.} and Dower, {Peter M.} and Iman Shames",

note = "Publisher Copyright: Copyright {\textcopyright} 2020 The Authors. This is an open access article under the CC BY-NC-ND license; 21st IFAC World Congress 2020 ; Conference date: 12-07-2020 Through 17-07-2020",

year = "2020",

doi = "10.1016/j.ifacol.2020.12.1764",

language = "English",

volume = "53",

pages = "6334--6339",

journal = "IFAC-PapersOnLine",

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TY - JOUR

T1 - Newton's method

T2 - 21st IFAC World Congress 2020

AU - Colabufo, Giuseppe G.

AU - Dower, Peter M.

AU - Shames, Iman

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - Incremental ISS (δISS)

KW - Input-to-state stability (ISS)

KW - Integral ISS (iISS)

KW - Newton's method

KW - Numerical methods

KW - Robust stability

UR - http://www.scopus.com/inward/record.url?scp=85105077142&partnerID=8YFLogxK

U2 - 10.1016/j.ifacol.2020.12.1764

DO - 10.1016/j.ifacol.2020.12.1764

M3 - Conference article

AN - SCOPUS:85105077142

SN - 2405-8963

VL - 53

SP - 6334

EP - 6339

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

IS - 2

Y2 - 12 July 2020 through 17 July 2020

ER -

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

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