Extending the applicability of the MMN-HSS method for solving systems of nonlinear equations under generalized conditions
type: Item
instance of: scholarly article
title: Extending the applicability of the MMN-HSS method for solving systems of nonlinear equations under generalized conditions
zbMATH Open document ID: 1461.65084
author: Ioannis Konstantinos Argyros
author: Janak Raj Sharma
author: Deepak Kumar
published in: Algorithms
publication date: 2018-08-20T00:00:00Z
review text: Summary: We present the semilocal convergence of a multi-step modified Newton-Hermitian and Skew-Hermitian Splitting method (MMN-HSS method) to approximate a solution of a nonlinear equation. Earlier studies show convergence under only Lipschitz conditions limiting the applicability of this method. The convergence in this study is shown under generalized Lipschitz-type conditions and restricted convergence domains. Hence, the applicability of the method is extended. Moreover, numerical examples are also provided to show that our results can be applied to solve equations in cases where earlier study cannot be applied. Furthermore, in the cases where both old and new results are applicable, the latter provides a larger domain of convergence and tighter error bounds on the distances involved.
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 6920640
zbMATH Keywords: MMN-HSS method
zbMATH Keywords: semilocal convergence
zbMATH Keywords: system of nonlinear equations
zbMATH Keywords: generalized Lipschitz conditions
zbMATH Keywords: Hermitian method
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3390/a10020054
OpenAlex ID: W2613068550
cites work: Geometric constructions of iterative functions to solve nonlinear equations
cites work: Dynamics of the King and Jarratt iterations
cites work: A modified Chebyshev's iterative method with at least sixth order of convergence
cites work: Convergence and Applications of Newton-type Iterations
cites work: On the local convergence of fast two-step Newton-like methods for solving nonlinear equations
cites work: Ball convergence theorems and the convergence planes of an iterative method for nonlinear equations
cites work: Local convergence of Newton-HSS methods with positive definite Jacobian matrices under generalized conditions
cites work: Iterative Solution Methods
cites work: On Newton-HSS Methods for Systems of Nonliear Equations with Positive-Definite Jacobian Matrices
cites work: Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hemitian positive semidefinite linear systems
cites work: Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
cites work: On the local convergence of a fifth-order iterative method in Banach spaces
cites work: Inexact Newton Methods
cites work: New iterations of \(R\)-order four with reduced computational cost
cites work: Recurrence relations for the super-Halley method
cites work: Semilocal and global convergence of the Newton-HSS method for systems of nonlinear equations.
cites work: On the semilocal convergence of a three steps Newton-type iterative process under mild convergence conditions
cites work: Multi-step modified Newton-HSS methods for systems of nonlinear equations with positive definite Jacobian matrices
cites work: Q5652137
cites work: Convergence criterion of inexact methods for operators with Hölder continuous derivatives
cites work: Convergence analysis of modified Newton-HSS method for solving systems of nonlinear equations
DOI: 10.3390/A10020054
description: scientific article; zbMATH DE number 6920640