A technique to choose the most efficient method between secant method and some variants

DOI10.1016/j.amc.2011.12.011zbMath1277.65032OpenAlexW2029072028MaRDI QIDQ422885

Miquel Noguera, Miquel Grau-Sánchez

Publication date: 18 May 2012

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2011.12.011

zbMATH Keywords

efficiencysymbolic computationiterative methodsnonlinear equationsorder of convergencesecant methoddivided difference

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Numerical computation of solutions to single equations (65H05)

Related Items (20)

An efficient derivative free family of fourth order methods for solving systems of nonlinear equations ⋮ Efficient derivative-free numerical methods for solving systems of nonlinear equations ⋮ Semilocal convergence of a secant-type method under weak Lipschitz conditions in Banach spaces ⋮ Note on the efficiency of some iterative methods for solving nonlinear equations ⋮ Seventh-order derivative-free iterative method for solving nonlinear systems ⋮ A study of optimization for Steffensen-type methods with frozen divided differences ⋮ An improvement of the Kurchatov method by means of a parametric modification ⋮ A multidimensional generalization of some classes of free-derivative iterative methods to solve nonlinear equations ⋮ A multidimensional generalization of some classes of iterative methods ⋮ A novel derivative free algorithm with seventh order convergence for solving systems of nonlinear equations ⋮ Multi-step derivative-free preconditioned Newton method for solving systems of nonlinear equations ⋮ Frozen iterative methods using divided differences ``à la Schmidt-Schwetlick ⋮ On the local convergence of a family of two-step iterative methods for solving nonlinear equations ⋮ Semilocal convergence of secant-like methods for differentiable and nondifferentiable operator equations ⋮ An efficient family of Traub-Steffensen-type methods for solving systems of nonlinear equations ⋮ On new computational local orders of convergence ⋮ On some efficient derivative-free iterative methods with memory for solving systems of nonlinear equations ⋮ On Convergence and Efficiency in the Resolution of Systems of Nonlinear Equations from a Local Analysis ⋮ Efficient higher order derivative-free multipoint methods with and without memory for systems of nonlinear equations ⋮ A simple yet efficient derivative free family of seventh order methods for systems of nonlinear equations

Uses Software

• MPFR

Cites Work

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• Frozen divided difference scheme for solving systems of nonlinear equations
• On some computational orders of convergence
• Geometric constructions of iterative functions to solve nonlinear equations
• On a higher order secant method.
• Secant-like methods for solving nonlinear integral equations of the Hammerstein type
• Computational theory of iterative methods.
• MPFR
• A variant of Newton's method with accelerated third-order convergence

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