Results 51 to 60 of about 205,428 (139)

An Iteration Function Having Optimal Eighth-Order of Convergence for Multiple Roots and Local Convergence

Mathematics, 2020
In the study of dynamics of physical systems an important role is played by symmetry principles. As an example in classical physics, symmetry plays a role in quantum physics, turbulence and similar theoretical models.
Ramandeep Behl, Ioannis K. Argyros, Michael Argyros, Mehdi Salimi, Arwa Jeza Alsolami   +4 more
doaj   +1 more source

Local Convergence Balls for Nonlinear Problems with Multiplicity and Their Extension to Eighth‐Order Convergence

Mathematical Problems in Engineering, Volume 2019, Issue 1, 2019., 2019
The main contribution of this study is to present a new optimal eighth‐order scheme for locating zeros with multiplicity m ≥ 1. An extensive convergence analysis is presented with the main theorem in order to demonstrate the optimal eighth‐order convergence of the proposed scheme.
Ramandeep Behl, Eulalia Martínez, Fabricio Cevallos, Ali S. Alshomrani, Changzhi Wu   +4 more
wiley   +1 more source

Efficacy of Optimal Methods for Nonlinear Equations with Chemical Engineering Applications

Mathematical Problems in Engineering, Volume 2019, Issue 1, 2019., 2019
In this study, we propose a modified predictor‐corrector Newton‐Halley (MPCNH) method for solving nonlinear equations. The proposed sixteenth‐order MPCNH is free of second derivatives and has a high efficiency index. The convergence analysis of the modified method is discussed.
Obadah Said Solaiman, Ishak Hashim, Xianming Zhang   +2 more
wiley   +1 more source

Optimal order and efficiency for iterations with two evaluations

, 1976
. The problem is to calculate a simple zero of a nonlinear function f. We consider rational iterations without memory which use two evaluations of f or its derivatives. It is shown that the optimal order is 2.
Kung, H.T., H. T. Kung, Traub, Josephe F., J. F. Traub   +3 more
core   +1 more source

Dynamical Techniques for Analyzing Iterative Schemes with Memory

Complexity, Volume 2018, Issue 1, 2018., 2018
We construct a new biparametric three‐point method with memory to highly improve the computational efficiency of its original partner, without adding functional evaluations. In this way, through different estimations of self‐accelerating parameters, we have modified an existing seventh‐order method.
Neha Choubey, A. Cordero, J. P. Jaiswal, J. R. Torregrosa, Peter Giesl   +4 more
wiley   +1 more source

New Iterative Procedures for Approximating Different Types of Inverse Matrix: Convergence and Stability

Mathematical Methods in the Applied Sciences, Volume 48, Issue 8, Page 8806-8817, 30 May 2025.
ABSTRACT In this paper, we propose a new parametric family of iterative schemes to compute the inverse of a complex nonsingular matrix. It is shown that the members of this family have at least a fourth order of convergence. A particular element of the class is extended to approximate the Moore–Penrose inverse of rectangular complex matrices, keeping ...
Alicia Cordero, Elaine Segura, Juan R. Torregrosa, María P. Vassileva   +3 more
wiley   +1 more source

Constructing a High‐Order Globally Convergent Iterative Method for Calculating the Matrix Sign Function

Mathematical Problems in Engineering, Volume 2018, Issue 1, 2018., 2018
This work is concerned with the construction of a new matrix iteration in the form of an iterative method which is globally convergent for finding the sign of a square matrix having no eigenvalues on the axis of imaginary. Toward this goal, a new method is built via an application of a new four‐step nonlinear equation solver on a particulate matrix ...
Haifa Bin Jebreen, Alberto Cavallo
wiley   +1 more source

Using decomposition of the nonlinear operator for solving non‐differentiable problems

Mathematical Methods in the Applied Sciences, Volume 48, Issue 7, Page 7987-8006, 15 May 2025.
Starting from the decomposition method for operators, we consider Newton‐like iterative processes for approximating solutions of nonlinear operators in Banach spaces. These iterative processes maintain the quadratic convergence of Newton's method.
Eva G. Villalba, Miguel Hernandez, Jose L. Hueso, Eulalia Martínez   +3 more
wiley   +1 more source

King‐Type Derivative‐Free Iterative Families: Real and Memory Dynamics

Complexity, Volume 2017, Issue 1, 2017., 2017
A biparametric family of derivative‐free optimal iterative methods of order four, for solving nonlinear equations, is presented. From the error equation of this class, different families of iterative schemes with memory can be designed increasing the order of convergence up to six.
F. I. Chicharro, A. Cordero, J. R. Torregrosa, M. P. Vassileva, Guido Caldarelli   +4 more
wiley   +1 more source

Sixteenth-Order Steffensen-Ostrowski Approach for Nonlinear Problems with ​A​pplications in Celestial, Predator-Prey and Neural Activation​

European Journal of Pure and Applied Mathematics
The increasing demand for accurate and effective approaches to complicated nonlinear models, driven by progress in diverse research and engineering fields, underscores the importance of tackling this challenge.
Saima Akram, Muhammad Bilal Riaz, F. Akram, F. Amir, Hareem Khalid, D. S. Sobirovich   +5 more
semanticscholar   +1 more source