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Acceleration of Newton's method for nonlinear algebraic systems by preflattening and elimination techniques
arXiv cs.NA0 views
arXiv:2610.11912v1 Announce Type: new Abstract: In this paper, we propose a new approach called {\em preflattening} to speed up the resolution of nonlinear algebraic systems by Newton-type methods. Preflattening is meant to be for nonlinear systems what preconditioning is for linear ones. The idea is to transform the system into an equivalent one that is more favorable to Newton's method. To this end, we introduce the notion of {\em flatness}, which is intended to play for nonlinear systems a role similar to that of the condition number for linear systems. For a physical model of interest in the geosciences, namely the chemical equilibrium problem, we combine this strategy with the nonlinear elimination technique and demonstrate the value of the resulting approach through numerical simulations.
Source：https://arxiv.org/abs/2610.11912PreviousBoundary integral equation based solvers for elastic transmission problems in complex mediaNextData-Driven Free-Energy Learning from Trajectories via Structure-Preserving Exponential Time Differencing
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