A variant of Newton's method with accelerated third-order convergence
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Publication:5931725
DOI10.1016/S0893-9659(00)00100-2zbMath0973.65037OpenAlexW2054711601WikidataQ126645325 ScholiaQ126645325MaRDI QIDQ5931725
S. Weerakoon, T. G. I. Fernando
Publication date: 25 April 2001
Published in: Applied Mathematics Letters (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0893-9659(00)00100-2
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methods with high efficiency index for solving nonlinear equations, Sixteenth-order method for nonlinear equations, A family of three-point methods of optimal order for solving nonlinear equations, Accelerated methods of order \(2p\) for systems of nonlinear equations, The Fibonacci family of iterative processes for solving nonlinear equations, Multipoint iterative method with cubic convergence, Construction of Newton-like iteration methods for solving nonlinear equations, A modification of Newton method with third-order convergence, Local convergence of a family of iterative methods for Hammerstein equations, Local convergence and a chemical application of derivative free root finding methods with one parameter based on interpolation, Variants of Newton's method for functions of several variables, Improved Newton iteration for nonlinear matrix equations on quadratic Lie groups, An analysis of the properties of the variants of Newton's method with third order convergence, Modified Halley's method free from second derivative, Analysing the efficiency of some modifications of the secant method, An iterative method for solving nonlinear equations, A note on some recent methods for solving nonlinear equations, A variant of Chebyshev's method with sixth-order convergence, Newton-Kantorovich convergence theorem of a modified Newton's method under the gamma-condition in a Banach space, Fourth- and fifth-order methods for solving nonlinear systems of equations: an application to the global positioning system, Means based modifications of Newton's method for solving nonlinear equations, A variant of super-Halley method with accelerated fourth-order convergence, A composite fourth-order iterative method for solving nonlinear equations, Fourth-order iterative methods free from second derivative, Construction of optimal order nonlinear solvers using inverse interpolation, A family of composite fourth-order iterative methods for solving nonlinear equations, Modified Chebyshev's method free from second derivative for non-linear equations, Pseudocomposition: A technique to design predictor-corrector methods for systems of nonlinear equations, Solving nonsmooth equations using family of derivative-free optimal methods, A modified secant method for unconstrained optimization, A weighted variant family of Newton's method with accelerated third-order convergence, A class of exponential quadratically convergent iterative formulae for unconstrained optimization, A family of fifth-order iterations composed of Newton and third-order methods, Frozen divided difference scheme for solving systems of nonlinear equations, Various Newton-type iterative methods for solving nonlinear equations, A new modified secant-like method for solving nonlinear equations, Sixth-order modifications of Newton's method based on Stolarsky and Gini means, Ball convergence theorems for eighth-order variants of Newton's method under weak conditions, An efficient family of optimal fourth-order iterative methods for finding multiple roots of nonlinear equations, A family of iterative methods that uses divided differences of first and second orders, Efficient high-order methods based on golden ratio for nonlinear systems, Iterative methods for use with nonlinear discrete algebraic models, A family of iterative methods with sixth and seventh order convergence for nonlinear equations, Improved local analysis for a certain class of iterative methods with cubic convergence, Some new iterative methods for nonlinear equations, Steffensen type methods for solving nonlinear equations, Two new classes of optimal Jarratt-type fourth-order methods, Eighth-order iterative methods without derivatives for solving nonlinear equations, A technique to choose the most efficient method between secant method and some variants, Variants of a classic Traub's result, The convergence of the perturbed Newton method and its application for ill-conditioned problems, Ball comparison between two optimal eight-order methods under weak conditions, A new optimal eighth-order family of iterative methods for the solution of nonlinear equations, Local convergence of efficient secant-type methods for solving nonlinear equations, Further development of Jarratt method for solving nonlinear equations, New eighth-order derivative-free methods for solving nonlinear equations, On a 4-point sixteenth-order King family of iterative methods for solving nonlinear equations, On iterative methods with accelerated convergence for solving systems of nonlinear equations, A new optimal eighth-order Ostrowski-type family of iterative methods for solving nonlinear equations, Accurate fourteenth-order methods for solving nonlinear equations, Numerical solution of nonlinear equations by an optimal eighth-order class of iterative methods, On the computational efficiency index and some iterative methods for solving systems of nonlinear equations, A comparison between iterative methods by using the basins of attraction, A new sixth-order scheme for nonlinear equations, Higher-order efficient class of Chebyshev-Halley type methods, Higher order iterative schemes for nonlinear equations using decomposition technique, An efficient three-step method to solve system of nonlinear equations, Third order derivative free SPH iterative method for solving nonlinear systems, New three- and four-parametric iterative with memory methods with efficiency index near 2, A class of efficient quadrature-based predictor-corrector methods for solving nonlinear systems, Enlarging the convergence domain in local convergence studies for iterative methods in Banach spaces, On a two-parameter Chebyshev-Halley-like family of optimal two-point fourth order methods free from second derivatives, Efficient derivative-free variants of Hansen-Patrick's family with memory for solving nonlinear equations, Multipoint methods for solving nonlinear equations: a survey, On a general class of optimal order multipoint methods for solving nonlinear equations, On the efficiency of a family of Steffensen-like methods with frozen divided differences, Semilocal convergence of secant-like methods for differentiable and nondifferentiable operator equations, Finite-element approximation for singularly perturbed nonlinear elliptic boundary-value problems, New third and fourth order nonlinear solvers for computing multiple roots, A new eighth-order iterative method for solving nonlinear equations, On convergence of a new secant-like method for solving nonlinear equations, On new computational local orders of convergence, A new general eighth-order family of iterative methods for solving nonlinear equations, A new method of secant-like for nonlinear equations, Some eighth-order root-finding three-step methods, A novel family of weighted-Newton optimal eighth order methods with dynamics, Certain improvements of Newton's method with fourth-order convergence, Third order iterative methods free from second derivative for nonlinear systems, How to increase convergence order of the Newton method to \(2\times m\)?, Iterative methods improving Newton's method by the decomposition method, On some third-order iterative methods for solving nonlinear equations
Cites Work
