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Masetti G., Chiaradonna S., Di Giandomenico F. Exploring equations ordering influence on variants of the Newton-Raphson method. In: NUMTA 2016 - 2ND International Conference "Numerical Computations: Theory and Algorithms" (Pizzo Calabro, Italy, 19-25 June 2016). Proceedings, article n. 090053. Yaroslav D. Sergeyev , Dmitri E. Kvasov , Francesco Dell’Accio, Marat S. Mukhametzhanov (eds.). (AIP Conference Proceedings, vol. 1776). AIP Publishing, 2016.
 
 
Abstract
(English)
Jacobian-free Newton-Raphson methods are general purpose iterative non-linear system solvers. The need to solve non-linear systems is ubiquitous throughout computational physics [1] and Jacobian-free Newton-Raphson methods can o er scalability, super-linear convergence and applicability. In fact, applications span from discretized PDEs [2] to power-flow problems [3]. The focus of this article is on Inexact-Newton-Krylov [2] and Quasi-Inverse-Newton [4] methods. For both of them, we prove analytically that the initial ordering of the equations can have a great impact on the numerical solution, as well as on the number of iterations to reach the solution. We also present numerical experiments for a small dimension case study in order to quantify the impact of initial equations ordering on a concrete scenario.
URL: http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.4965417
DOI: http://dx.doi.org/10.1063/1.4965417
Subject Newton-Raphson methods
Equation ordering
G.1 NUMERICAL ANALYSIS
65 - Numerical analysis


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