Results 1 to 10 of about 199 (61)

Ball convergence of Potra-Ptak-type method with optimal fourth order of convergence

Journal of Numerical Analysis and Approximation Theory, 2021
We present a local convergence analysis Potra-Ptak-type method with optimal fourth order of convergence in order to approximate a solution of a nonlinear equation. In earlier studies such as [1], [5]-[28] hypotheses up to the fourth derivative are used.
Ioannis K. Argyros, Santhosh George
doaj   +7 more sources

On the Local Convergence of Two-Step Newton Type Method in Banach Spaces under Generalized Lipschitz Conditions

Mathematics, 2021
The motive of this paper is to discuss the local convergence of a two-step Newton-type method of convergence rate three for solving nonlinear equations in Banach spaces.
Akanksha Saxena, Ioannis K. Argyros, Jai P. Jaiswal, Christopher Argyros, Kamal R. Pardasani   +4 more
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Semi-Local Convergence of a Seventh Order Method with One Parameter for Solving Non-Linear Equations

Foundations, 2022
The semi-local convergence is presented for a one parameter seventh order method to obtain solutions of Banach space valued nonlinear models. Existing works utilized hypotheses up to the eighth derivative to prove the local convergence.
Christopher I. Argyros, Ioannis K. Argyros, Samundra Regmi, Jinny Ann John, Jayakumar Jayaraman   +4 more
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Semi-Local Convergence of Two Derivative-Free Methods of Order Six for Solving Equations under the Same Conditions

Foundations, 2022
We propose the semi-local convergence of two derivative-free, competing methods of order six to address non-linear equations. The sufficient convergence criteria are the same, making a direct comparison between them possible.
Ioannis K. Argyros, Christopher I. Argyros, Jinny Ann John, Jayakumar Jayaraman   +3 more
doaj   +1 more source

Ball Comparison between Two Efficient Weighted-Newton-like Solvers for Equations

Foundations, 2022
We compare the convergence balls and the dynamical behaviors of two efficient weighted-Newton-like equation solvers by Sharma and Arora, and Grau-Sánchez et al.
Ioannis K. Argyros, Samundra Regmi, Christopher I. Argyros, Debasis Sharma   +3 more
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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, Stepan M. Shakhno, Yurii Shunkin, Halyna Yarmola   +3 more
doaj   +7 more sources

Extended Comparison between Two Derivative-Free Methods of Order Six for Equations under the Same Conditions

Fractal and Fractional, 2022
Under the same conditions, we propose the extended comparison between two derivative free schemes of order six for addressing equations. The existing convergence technique used the standard Taylor series approach, which requires derivatives up to order ...
Samundra Regmi, Ioannis K. Argyros, Christopher I. Argyros, Debasis Sharma   +3 more
doaj   +1 more source

On the Semi-Local Convergence of Two Competing Sixth Order Methods for Equations in Banach Space

Algorithms, 2022
A plethora of methods are used for solving equations in the finite-dimensional Euclidean space. Higher-order derivatives, on the other hand, are utilized in the calculation of the local convergence order. However, these derivatives are not on the methods.
Ioannis K. Argyros, Stepan Shakhno, Samundra Regmi, Halyna Yarmola   +3 more
doaj   +1 more source

Ball Convergence for Steffensen-type Fourth-order Methods

International Journal of Interactive Multimedia and Artificial Intelligence, 2015
We present a local convergence analysis for a family of Steffensen-type fourth-order methods in order to approximate a solution of a nonlinear equation.
Ioannis K. Argyros, Santhosh George
doaj   +1 more source

Extended High Order Algorithms for Equations under the Same Set of Conditions

Algorithms, 2021
A variety of strategies are used to construct algorithms for solving equations. However, higher order derivatives are usually assumed to calculate the convergence order.
Ioannis K. Argyros, Debasis Sharma, Christopher I. Argyros, Sanjaya Kumar Parhi, Shanta Kumari Sunanda, Michael I. Argyros   +5 more
doaj   +1 more source