Zobrazeno 1 - 10
of 61
pro vyhledávání: '"Christopher I. Argyros"'
Publikováno v:
Algorithms, Vol 17, Iss 4, p 154 (2024)
Iterative algorithms requiring the computationally expensive in general inversion of linear operators are difficult to implement. This is the reason why hybrid Newton-like algorithms without inverses are developed in this paper to solve Banach space-
Externí odkaz:
https://doaj.org/article/fd2b09d417114f5a97d7e449ce931aba
Publikováno v:
Foundations, Vol 2, Iss 4, Pp 1022-1030 (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. The existing convergence
Externí odkaz:
https://doaj.org/article/2e1055c7d51044bda016f70cb2c83fc9
Publikováno v:
Foundations, Vol 2, Iss 4, Pp 1031-1044 (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. First of all, the results of ball convergence for these algorithms are established by em
Externí odkaz:
https://doaj.org/article/ea0babbaea1d4fee9613c9c72ef6f5cf
Semi-Local Convergence of a Seventh Order Method with One Parameter for Solving Non-Linear Equations
Autor:
Christopher I. Argyros, Ioannis K. Argyros, Samundra Regmi, Jinny Ann John, Jayakumar Jayaraman
Publikováno v:
Foundations, Vol 2, Iss 4, Pp 827-838 (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. But these hig
Externí odkaz:
https://doaj.org/article/43c030d25c434fc99ec0e46ca9d45342
Publikováno v:
Fractal and Fractional, Vol 6, Iss 11, p 634 (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 ord
Externí odkaz:
https://doaj.org/article/dadcd96675f74aeda13bb7cf0b2b4532
Publikováno v:
Symmetry, Vol 14, Iss 7, p 1484 (2022)
Symmetries are vital in the study of physical phenomena such as quantum physics and the micro-world, among others. Then, these phenomena reduce to solving nonlinear equations in abstract spaces. These equations in turn are mostly solved iteratively.
Externí odkaz:
https://doaj.org/article/94c4f45bc94a4b44861de772433cbb2e
Publikováno v:
Axioms, Vol 11, Iss 7, p 307 (2022)
In this article, we present generalized conditions of three-step iterative schemes for solving nonlinear equations. The convergence order is shown using Taylor series, but the existence of high-order derivatives is assumed. However, only the first de
Externí odkaz:
https://doaj.org/article/c841145d208f4e869f1591e1500b664b
Publikováno v:
European Journal of Mathematical Analysis, Vol 2, Pp 18-18 (2022)
The semi-local convergence criteria for Newton’s method are weakened without new conditions. Moreover, tighter error distances are provided as well as a more precise information on the location of the solution.
Externí odkaz:
https://doaj.org/article/525a3276d9f040a68e5a3d58633c9cbe
Publikováno v:
Mathematics, Vol 10, Iss 8, p 1225 (2022)
There are a plethora of semi-local convergence results for Newton’s method (NM). These results rely on the Newton–Kantorovich criterion. However, this condition may not be satisfied even in the case of scalar equations. For this reason, we first
Externí odkaz:
https://doaj.org/article/88cfe51b4cd04d9f93919230b60254dd
Publikováno v:
Mathematics, Vol 9, Iss 23, p 3106 (2021)
We develop a unified convergence analysis of three-step iterative schemes for solving nonlinear Banach space valued equations. The local convergence order has been shown before to be five on the finite dimensional Euclidean space assuming Taylor expa
Externí odkaz:
https://doaj.org/article/2b1b8ec22d11485bb4aa07fcaf4b535e