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We study the local order of convergence of the new iterative methods with memory.
In this paper, we analyze the stability of a parametric family of iterative methods with memory for solving nonlinear equations.
A dynamical approach on the dynamics of iterative methods with memory for solving nonlinear equations is made.
The role of the derivatives at the iterative expression of methods with memory for solving nonlinear equations is analyzed in this manuscript.
In the literature exist many iterative methods with memory for solving nonlinear equations, the most of them designed in the last years.
We have designed new methods with memory from Steffensen' or Traub's schemes, as well as from a parametric family of iterative procedures of third- and fourth-order of convergence.
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The use of adapted methods with low memory storage (Low storage Runge Kutta methods) gives good results for low precision studies, whereas the Taylor series method provides a powerful technique for high precision.
This super-cubic convergence is obtained by self-accelerating second-order Steffensen's method twice with memory, but without any new function evaluations.
Our proposal aims to develop a method with lower memory overhead than the Alg Hung algorithm, while reducing the probable increase in delta size when compared with Alg Sign.
First, we extend the statistical physics method of invasion percolation with memory, which models lattice problems with thresholds, to incorporate dynamic effects due to the viscous friction following the onset of mobilization.
The methods for identification of static nonlinearities indeed do not require the same level of model complexity as methods used for nonlinear systems with memory or with gain control.
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