Local convergence balls for nonlinear problems with multiplicity and their extension to eighth-order convergence

DOI10.1155/2019/1427809zbMath1435.65073OpenAlexW2907945140MaRDI QIDQ2298057

Eulalia Martínez, Ramandeep Behl, Ali Saleh Alshomrani, Fabricio Cevallos

Publication date: 20 February 2020

Published in: Mathematical Problems in Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2019/1427809

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Numerical computation of solutions to single equations (65H05) Numerical computation of roots of polynomial equations (65H04)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convergence radius of Osada's method under center-Hölder continuous condition
• An optimal fourth-order family of methods for multiple roots and its dynamics
• An analysis of a family of Maheshwari-based optimal eighth order methods
• Introduction to higher-order iterative methods for finding multiple roots of nonlinear equations
• Families of third and fourth order methods for multiple roots of nonlinear equations
• On a numerical technique for finding multiple zeros and its dynamic
• Finding the solution of nonlinear equations by a class of optimal methods
• Constructing higher-order methods for obtaining the multiple roots of nonlinear equations
• Convergence of the modified Halley's method for multiple zeros under Hölder continuous derivative
• A class of two-point sixth-order multiple-zero finders of modified double-Newton type and their dynamics
• Constructing a family of optimal eighth-order modified Newton-type multiple-zero finders along with the dynamics behind their purely imaginary extraneous fixed points
• A study of dynamics via Möbius conjugacy map on a family of sixth-order modified Newton-like multiple-zero finders with bivariate polynomial weight functions
• A new fourth-order iterative method for finding multiple roots of nonlinear equations
• Some fourth-order nonlinear solvers with closed formulae for multiple roots
• Optimal iterative methods for finding multiple roots of nonlinear equations using free parameters
• On developing fourth-order optimal families of methods for multiple roots and their dynamics
• A sixth-order family of three-point modified Newton-like multiple-root finders and the dynamics behind their extraneous fixed points
• Application of interval Newton's method to chemical engineering problems
• On the convergence radius of the modified Newton method for multiple roots under the center-Hölder condition
• Determination of multiple roots of nonlinear equations and applications
• Variants of Newton's method using fifth-order quadrature formulas
• Extension of Murakami's high-order non-linear solver to multiple roots
• On The Convergence And Application Of Newton's Method Under Weak HÖlder Continuity Assumptions
• Optimal Order of One-Point and Multipoint Iteration

This page was built for publication: Local convergence balls for nonlinear problems with multiplicity and their extension to eighth-order convergence