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

A. Fischer (), A. F. Izmailov () and M. V. Solodov ()
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A. Fischer: Technische Universität Dresden
A. F. Izmailov: Lomonosov Moscow State University, MSU
M. V. Solodov: IMPA – Instituto de Matemática Pura e Aplicada

Computational Optimization and Applications, 2021, vol. 78, issue 1, No 9, 273-286

Abstract: 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.

Keywords: Nonlinear equation; Newton method; Singular solution; Critical solution; 2-regularity; Linear convergence; Superlinear convergence; Extrapolation; Overrelaxation; Linesearch; 65H10; 65H20 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10589-020-00230-x

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