Results 11 to 20 of about 470,890 (244)
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 +1 more source
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
Unified Convergence Criteria of Derivative-Free Iterative Methods for Solving Nonlinear Equations
Computation, 2023 A local and semi-local convergence is developed of a class of iterative methods without derivatives for solving nonlinear Banach space valued operator equations under the classical Lipschitz conditions for first-order divided differences.
Samundra Regmi +3 more
doaj +1 more source
Extended convergence analysis of Newton-Potra solver for equations
Journal of Numerical Analysis and Approximation Theory, 2020 In the paper a local and a semi-local convergence of combined iterative process for solving nonlinear operator equations is investigated. This solver is built based on Newton solver and has R-convergence order 1.839....
Ioannis Argyros +3 more
doaj +7 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 +1 more source
A decorated tree approach to random permutations in substitution-closed classes [PDF]
, 2020 We establish a novel bijective encoding that represents permutations as forests of decorated (or enriched) trees. This allows us to prove local convergence of uniform random permutations from substitution-closed classes satisfying a criticality ...
Borga, Jacopo +3 more
core +5 more sources