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SEMI-LOCAL CONVERGENCE OF A DERIVATIVE-FREEMETHOD FOR SOLVING EQUATIONS
Проблемы анализа, 2021 We present the semi-local convergence analysis of atwo-step derivative-free method for solving Banach space valuedequations. The convergence criteria are based only on the firstderivative and our idea of recurrent functions.
Gus Argyros +3 more
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On the Semi-Local Convergence of a Third Order Scheme for Solving Nonlinear Equations
European Journal of Mathematical Analysis, 2022 The semi-local convergence analysis of a third order scheme for solving nonlinear equation in Banach space has not been given under Lipschitz continuity or other conditions.
Samundra Regmi +3 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 +4 more
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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 +3 more
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Mathematics, 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.
Samundra Regmi +3 more
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On the semi-local convergence of a sixth order method in Banach space
Journal of Numerical Analysis and Approximation Theory, 2022 High convergence order methods are important in computational mathematics, since they generate sequences converging to a solution of a non-linear equation.
Ioannis K Argyros +2 more
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Improved semi-local convergence of the Gauss-Newton method for systems of equations
Journal of Mathematical Sciences and Modelling, 2018 Our new technique of restricted convergence domains is employed to provide a finer convergence analysis of the Gauss-Newton method in order to solve a certain class of systems of equations under a majorant condition. The advantages are obtained under the
Santhosh George, İoannis K Argyros
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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 +3 more
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Local and semi-local convergence analysis of a multi-step method [PDF]
Electronic Journal of MathematicsIoannis K. Argyros +3 more
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SEMI-LOCAL CONVERGENCE OF A SEVENTH-ORDER METHOD IN BANACH SPACES UNDER ω-CONTINUITY CONDITION [PDF]
Surveys in Mathematics and its Applications, 2020 The article is about the analysis of semi-local convergence of a seventh-order iterative method used for finding the roots of a nonlinear equation in Banach spaces.
Neha Gupta, Jai Prakash Jaiswal
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