Multidimensional Real Dynamics for High-Order Processes

  • Alicia CorderoEmail author
  • Javier G. Maimó
  • Juan R. Torregrosa
  • Maria P. Vassileva
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)


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.


Nonlinear 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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Instituto Universitario de Matemática MultidisciplinarUniversitat Politècnica de ValènciaValènciaSpain
  2. 2.Instituto Tecnológico de Santo DomingoSanto DomingoDominican Republic

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