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Nondiscrete induction and iterative processes
Florian A. Potra,Vlastimil Pták +1 more
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The article was published on 1984-01-01 and is currently open access. It has received 374 citations till now.read more
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Second-derivative free methods of third and fourth order for solving nonlinear equations
Janak Raj Sharma,Rangan K. Guha +1 more
TL;DR: A one-parameter family of iterative methods for solving nonlinear equations except the one which has the fourth-order convergence, which is shown to be more economic than the third-order methods.
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A two-parameter third-order family of methods for solving nonlinear equations
TL;DR: A new two-parameter family of iterative methods for solving nonlinear equations which includes, as a particular case, the classical Potra and Ptak third-order method is presented, showing that each family member is cubically convergent.
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Superconvergent Nyström method for Urysohn integral equations
TL;DR: In this article, a superconvergent Nystrom method has been used for solving one of the most important cases in nonlinear integral equations which is called Urysohn form, using an interpolatory projection at the set of r Gauss points, it is shown that the proposed method has an order of 3r and one step of iteration improve the convergence order to 4r.
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Secant method with regularly continuous divided differences
TL;DR: In this article, a convergence analysis of the secant method for solving nonlinear operator equations in Banach spaces using Kantorovich's technique of majorization is presented. But this analysis is based on a different continuity characteristic of the divided difference operator (called regular continuity) which is more general (but not too general) and more flexible than those used by other researchers.
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Sharp estimation of local convergence radius for the Picard iteration
Stefan Maruster,Laura Maruster +1 more
TL;DR: In this article, the authors investigated the local convergence radius of a general Picard iteration in the frame of a real Hilbert space and proposed a new algorithm to estimate the local local convergence.