Exploring equations ordering influence on variants of the Newton-Raphson method

Masetti G., Chiaradonna S., Di Giandomenico F.

Equation ordering  Newton-Raphson methods 

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 offer 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 results obtained from a simple but representative case study, to quantify the impact of initial equations ordering on a concrete scenario.

Source: 2ND International Conference "Numerical Computations: Theory and Algorithms", pp. 090053–090055, Pizzo Calabro, Italy, 19-25 June 2016

Publisher: American Institute of Physics,, New York , Stati Uniti d'America

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