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Ioannis K. Argyros, Santhosh George, Samundra Regmi and Christopher I. Argyros
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-valu...
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Ioannis K. Argyros, Stepan Shakhno, Samundra Regmi and Halyna Yarmola
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...
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Ioannis K. Argyros, Debasis Sharma, Christopher I. Argyros, Sanjaya Kumar Parhi, Shanta Kumari Sunanda and Michael I. Argyros
A variety of strategies are used to construct algorithms for solving equations. However, higher order derivatives are usually assumed to calculate the convergence order. More importantly, bounds on error and uniqueness regions for the solution are also n...
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Janak Raj Sharma, Sunil Kumar and Ioannis K. Argyros
We discuss the local convergence of a derivative-free eighth order method in a Banach space setting. The present study provides the radius of convergence and bounds on errors under the hypothesis based on the first Fréchet-derivative only. The approaches...
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