Accelerating convergence of the globalized Newton method to critical solutions of nonlinear equations

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Abstract

In the case of singular (and possibly even nonisolated) solutions of nonlinear equations, while superlinear convergence of the Newton method cannot be guaranteed, local linear convergence from large domains of starting points still holds under certain reasonable assumptions.We consider a linesearch globalization of the Newton method, combined with extrapolation and over-relaxation accelerating techniques, aiming at a speed up of convergence to critical solutions (a certain class of singular solutions). Numerical results indicate that an acceleration is observed indeed.

Details

Original languageEnglish
Pages (from-to)273-286
Number of pages14
JournalComputational Optimization and Applications
Volume78
Issue number1
Publication statusPublished - Jan 2021
Peer-reviewedYes

External IDs

Scopus 85091299963
Mendeley c3dccf97-eb20-321d-b05e-8002b1a9f748

Keywords

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