Results 11 to 20 of about 472,892 (253)
On the Semi-Local Convergence of a Fifth-Order Convergent Method for Solving Equations [PDF]
Foundations, 2022 We study the semi-local convergence of a three-step Newton-type method for solving nonlinear equations under the classical Lipschitz conditions for first-order derivatives. To develop a convergence analysis, we use the approach of restricted convergence regions in combination with majorizing scalar sequences and our technique of recurrent functions ...
Christopher I. Argyros +3 more
openaire +3 more sources
On the Semi-Local Convergence of a Jarratt-Type Family Schemes for Solving Equations [PDF]
Foundations, 2022 We study semi-local convergence of two-step Jarratt-type method for solving nonlinear equations under the classical Lipschitz conditions for first-order derivatives. To develop a convergence analysis we use the approach of restricted convergence regions in combination to majorizing scalar sequences and our technique of recurrent functions. Finally, the
Christopher I. Argyros +3 more
openaire +3 more sources
On the Semi-Local Convergence of a Noor–Waseem-like Method for Nonlinear Equations
Foundations, 2022 The significant feature of this paper is that the semi-local convergence of high order methods for solving nonlinear equations defined on abstract spaces has not been studied extensively as done for the local convergence by a plethora of authors which is certainly a more interesting case.
Ioannis K. Argyros +3 more
openaire +3 more sources
Unified Semi-Local Convergence for k—Step Iterative Methods with Flexible and Frozen Linear Operator [PDF]
Mathematics, 2018 The aim of this article is to present a unified semi-local convergence analysis for a k-step iterative method containing the inverse of a flexible and frozen linear operator for Banach space valued operators. Special choices of the linear operator reduce the method to the Newton-type, Newton’s, or Stirling’s, or Steffensen’s, or other methods.
Ioannis K. Argyros, Santhosh George
openaire +5 more sources
Journal of Computational and Applied Mathematics, 2015 A semi-local analysis of Newton's method for solving nonlinear inclusion problems in Banach space is presented in this paper. Under a affine majorant condition on the nonlinear function which is associated to the inclusion problem, the robust convergence of the method and results on the convergence rate are established.
Orizon Ferreira
openaire +5 more sources
On the Semi-Local Convergence of a Traub-Type Method for Solving Equations [PDF]
Foundations, 2022 The celebrated Traub’s method involving Banach space-defined operators is extended. The main feature in this study involves the determination of a subset of the original domain that also contains the Traub iterates. In the smaller domain, the Lipschitz constants are smaller too.
Samundra Regmi +3 more
openaire +1 more source
Convergence of Derivative-Free Iterative Methods with or without Memory in Banach Space
Foundations, 2023 A method without memory as well as a method with memory are developed free of derivatives for solving equations in Banach spaces. The convergence order of these methods is established in the scalar case using Taylor expansions and hypotheses on higher ...
Santhosh George +2 more
doaj +1 more source
On the convergence of Kurchatov-type methods using recurrent functions for solving equations
Математичні Студії, 2022 We study a local and semi-local convergence of Kurchatov's method and its two-step modification for solving nonlinear equations under the classical Lipschitz conditions for the first-order divided differences. To develop a convergence analysis we use the
I. K. Argyros, S. Shakhno, H. Yarmola
doaj +1 more source
Extended Convergence of Two Multi-Step Iterative Methods
Foundations, 2023 Iterative methods which have high convergence order are crucial in computational mathematics since the iterates produce sequences converging to the root of a non-linear equation. A plethora of applications in chemistry and physics require the solution of
Samundra Regmi +3 more
doaj +1 more source
On the Semi-Local Convergence of an Ostrowski-Type Method for Solving Equations [PDF]
Symmetry, 2021 Symmetries play a crucial role in the dynamics of physical systems. As an example, microworld and quantum physics problems are modeled on principles of symmetry. These problems are then formulated as equations defined on suitable abstract spaces. Then, these equations can be solved using iterative methods.
Christopher I. Argyros +4 more
openaire +1 more source