Multidimensional Real Dynamics for High-Order Processes
In this manuscript, we design a parametric family of iterative methods for solving nonlinear problems, that does not need to evaluate Jacobian matrices and needs to solve three linear systems per iteration with the same divided difference operator as coefficient matrix. The stability performance of the class is analyzed on a quadratic polynomial system and it is shown that for a wide set of values (including positive ones), there exist only convergence to the roots of the problem.
KeywordsNonlinear systems Real multidimensional dynamics Stability
This research was partially supported by Ministerio de Economia y Competitividad under grants MTM2014-52016-C2-2-P, Generalitat Valenciana PROMETEO/2016/089 and FONDOCYT, Dominican Republic.
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