48 research outputs found
A New Preconditioner on Gauss‐Seidel Method for H‐Matrices
In order to accelerate the convergency of Gauss‐Seidel method to solve systems of linear equations when the coefficient matrix is an H‐matrix, a new preconditioner is introduced. The convergency of the new preconditioned method is proved
Implication of BRCA2 -26G>A 5' untranslated region polymorphism in susceptibility to sporadic breast cancer and its modulation by p53 codon 72 Arg>Pro polymorphism
Memetic computing through bio-inspired heuristics integration with sequential quadratic programming for nonlinear systems arising in different physical models
A correction of (2+1) Dimensional BTZ Black Hole Entropy as a New Series with Dependence on Plank Constant
Forward scattering for non-linear wave propagation in (3 + 1)-dimensional Jimbo-Miwa equation using singular manifold and group transformation methods
Effects of Vacuum and Juice Concentration on Electrical Conductivity by the Ohmic Method: a Case Study of Sour Cherry
New fourth and sixth-order classes of iterative methods for solving systems of nonlinear equations and their stability analysis
[EN] In this paper, a two-step class of fourth-order iterative methods for solving systems of nonlinear equations is presented. We further extend the two-step class to establish a new sixth-order family which requires only one additional functional evaluation. The convergence analysis of the proposed classes is provided under several mild conditions. A complete dynamical analysis is made, by using real multidimensional discrete dynamics, in order to select the most stable elements of both families of fourth- and sixth-order of convergence. To get this aim, a novel tool based on the existence of critical points has been used, the parameter line. The analytical discussion of the work is upheld by performing numerical experiments on some application-oriented problems. We provide an implementation of the proposed scheme on nonlinear optimization problem and zero-residual nonlinear least-squares problems taken from the constrained and unconstrained testing environment test set. Finally, based on numerical results, it has been concluded that our methods are comparable with the existing ones of similar nature in terms of order, efficiency, and computational time and also that the stability results provide the most efficient member of each class of iterative schemes.This research was partially supported by PGC2018-095896-B-C22 (MCIU/AEI/FEDER, UE), Generalitat Valenciana PROMETEO/2016/089Kansal, M.; Cordero Barbero, A.; Bhalla, S.; Torregrosa Sánchez, JR. (2021). New fourth and sixth-order classes of iterative methods for solving systems of nonlinear equations and their stability analysis. Numerical Algorithms. 87(3):1017-1060. https://doi.org/10.1007/s11075-020-00997-4S1017106087