Extended ball convergence of a seventh order derivative free method for solving system of equations with applications

Argyros, Ioannis K.; Sharma, Debasis; Argyros, Christopher I.; Parhi, Sanjaya Kumar; Argyros, Michael I.

doi:10.1007/s41478-022-00453-7

Cited by 2 publications

(1 citation statement)

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“…The local convergence order q + 2 is determined in [23] by means of the Taylor expansion series approach when Q 1 = Q 2 = R k . Moreover, assumptions on the existence and boundedness of G (4) are required limiting the applicability of TSFM to solve equations with operators at least four times dierentiable. But TSFM may converge if only G ′ appearing on it exists.…”

Section: Introductionmentioning

confidence: 99%

Increased and Extended Convergence of a family of three-step methods

Argyros,

John,

Jayaraman

2023

J. App. Num. Analysis

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In various scientific and engineering disciplines, a wide range of applications can be simplified to the task of solving equations or systems of equations within a carefully selected abstract space. Due to the inherent dificulty or even impossibility of finding analytical solutions, iterative methods are commonly employed to obtain the desired solutions. This article focuses on the presentation of efficient family of three-step iterative methods that exhibit high convergence order. The analysis delves into the local and semi-local convergence properties, considering φ-continuity conditions imposed on the operators utilized. The novel methodology introduced in this article is not limited to specific methods but can be applied to a broader range of approaches that involve the use of inverses of linear operators or matrices.

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Section: Introductionmentioning

confidence: 99%