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Variants of Newton's Method using fifth-order quadrature formulas
Abstract Some variants of Newton’s method are developed in this work in order to solve nonlinear equations depending on one or several variables, based in rules of quadrature of fifth order. We proveExpand
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Steffensen type methods for solving nonlinear equations
In the present paper, by approximating the derivatives in the well known fourth-order Ostrowski's method and in a sixth-order improved Ostrowski's method by central-difference quotients, we obtainExpand
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A modified Newton-Jarratt’s composition
A reduced composition technique has been used on Newton and Jarratt’s methods in order to obtain an optimal relation between convergence order, functional evaluations and number of operations.Expand
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Variants of Newton's method for functions of several variables
Some variants of Newton's Method are developed in this work in order to solve systems of nonlinear equations, based in trapezoidal and midpoint rules of quadrature. We prove the quadratic convergenceExpand
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Increasing the convergence order of an iterative method for nonlinear systems
Abstract In this work we introduce a technique for solving nonlinear systems that improves the order of convergence of any given iterative method which uses the Newton iteration as a predictor. TheExpand
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Iterative methods of order four and five for systems of nonlinear equations
The Adomian decomposition is used in order to obtain a family of methods to solve systems of nonlinear equations. The order of convergence of these methods is proved to be p>=2, under the sameExpand
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Modified Newton's method for systems of nonlinear equations with singular Jacobian
It is well known that Newton's method for a nonlinear system has quadratic convergence when the Jacobian is a nonsingular matrix in a neighborhood of the solution. Here we present a modification ofExpand
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Pseudocomposition: A technique to design predictor-corrector methods for systems of nonlinear equations
Abstract A new technique for designing iterative methods for solving nonlinear systems is presented. This procedure, called pseudocomposition, uses a known method as a predictor and the GaussianExpand
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Three-step iterative methods with optimal eighth-order convergence
In this paper, based on Ostrowski's method, a new family of eighth-order methods for solving nonlinear equations is derived. In terms of computational cost, each iteration of these methods requiresExpand
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Optimal iterative methods for finding multiple roots of nonlinear equations using free parameters
In this paper, we propose a family of optimal eighth order convergent iterative methods for multiple roots with known multiplicity with the introduction of two free parameters and three univariateExpand
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