4 research outputs found
A new three-steps iterative method for solving nonlinear systems
No full textCapdevila, RR.; Cordero Barbero, A.; Torregrosa Sánchez, JR. (2019). A new three-steps iterative method for solving nonlinear systems. R. Company, J. C. Cortés, L. Jódar and E.López-Navarro. 22-25. https://riunet.upv.es/handle/10251/180675S222
Isonormal surfaces: A new tool for the multidimensional dynamical analysis of iterative methods for solving nonlinear systems
No full text[EN] The dynamical behavior of the rational vectorial operator associated with a multidimensional iterative method on polynomial systems gives us interesting information about the stability of the iterative scheme. The stability of fixed points, dynamic planes, bifurcation diagrams, etc. are known tools that provide us this information. In this manuscript, we introduce a new tool, which we call isonormal surface, to complement the information about the stability of the iterative method provided by the dynamical elements mentioned above. These dynamical instruments are used for analyzing the stability of a parametric family of multidimensional iterative schemes in terms of the value of the parameter. Some numerical tests confirm the obtained dynamical results.Ministerio de Ciencia, Innovacion y Universidades (MCIU/AEI/FEDER, UE), Grant/Award Number: PGC2018-095896-B-C22Capdevila-Brown, RR.; Cordero Barbero, A.; Torregrosa Sánchez, JR. (2022). Isonormal surfaces: A new tool for the multidimensional dynamical analysis of iterative methods for solving nonlinear systems. Mathematical Methods in the Applied Sciences. 45(6):3360-3375. https://doi.org/10.1002/mma.7695S3360337545
A new three-step class of iterative methods for solving nonlinear systems
No full text[EN] In this work, a new class of iterative methods for solving nonlinear equations is presented and also its extension for nonlinear systems of equations. This family is developed by using a scalar and matrix weight function procedure, respectively, getting sixth-order of convergence in both cases. Several numerical examples are given to illustrate the efficiency and performance of the proposed methods.This research has been partially supported by both Generalitat Valenciana and Ministerio de Ciencia, Investigacion y Universidades, under grants PROMETEO/2016/089 and PGC2018-095896-B-C22 (MCIU/AEI/FEDER, UE), respectively.Capdevila-Brown, RR.; Cordero Barbero, A.; Torregrosa Sánchez, JR. (2019). A new three-step class of iterative methods for solving nonlinear systems. Mathematics. 7(12):1-14. https://doi.org/10.3390/math7121221S11471
Convergence and dynamical study of a new sixth order convergence iterative scheme for solving nonlinear systems
No full text[EN] A novel family of iterative schemes to estimate the solutions of nonlinear systems is
presented. It is based on the Ermakov-Kalitkin procedure, which widens the set of converging initial
estimations. This class is designed by means of a weight function technique, obtaining 6th-order
convergence. The qualitative properties of the proposed class are analyzed by means of vectorial real
dynamics. Using these tools, the most stable members of the family are selected, and also the chaotical
elements are avoided. Some test vectorial functions are used in order to illustrate the performance and
efficiency of the designed schemesThis research was partially supported by Grant PGC2018-095896-B-C22 funded by MCIN/AEI/31000.13039/ ERDF A way to making Europe , European Union.Capdevila, RR.; Cordero Barbero, A.; Torregrosa Sánchez, JR. (2023). Convergence and dynamical study of a new sixth order convergence iterative scheme for solving nonlinear systems. AIMS Mathematics. 8(6):12751-12777. https://doi.org/10.3934/math.2023642S12751127778
