A family of iterative methods that uses divided differences of first and second orders

DOI10.1007/s11075-015-9962-0zbMath1329.65105OpenAlexW2056197860MaRDI QIDQ891783

Miquel Noguera, José Antonio Ezquerro, Miguel Ángel Hernández-Verón, Miquel Grau-Sánchez

Publication date: 17 November 2015

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/2117/80873

zbMATH Keywords

numerical exampleefficiencysystems of nonlinear equationsorder of convergencedivided differencenonlinear integral equation of mixed Hammerstein typefourth-order Steffensen-type derviative-free iterative methods

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Numerical methods for integral equations (65R20) Other nonlinear integral equations (45G10) Complexity and performance of numerical algorithms (65Y20)

Related Items (6)

On a two-step optimal Steffensen-type method: relaxed local and semi-local convergence analysis and dynamical stability ⋮ Unnamed Item ⋮ A family of higher order derivative free methods for nonlinear systems with local convergence analysis ⋮ A study on the local convergence and dynamics of the two-step and derivative-free Kung-Traub's method ⋮ A class of third order iterative Kurchatov-Steffensen (derivative free) methods for solving nonlinear equations ⋮ Higher-order modification of Steffensen's method for solving system of nonlinear equations

Uses Software

• MPFR

Cites Work

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• An efficient derivative free family of fourth order methods for solving systems of nonlinear equations
• An optimal Steffensen-type family for solving nonlinear equations
• Frozen divided difference scheme for solving systems of nonlinear equations
• On new computational local orders of convergence
• A two-step Steffensen's method under modified convergence conditions
• On some computational orders of convergence
• A variant of Steffensen's method of fourth-order convergence and its applications
• A class of two-step Steffensen type methods with fourth-order convergence
• The secant method and fixed points of nonlinear operators
• A family of Steffensen type methods with seventh-order convergence
• Computational theory of iterative methods.
• On a Steffensen's type method and its behavior for semismooth equations
• Efficient Steffensen-type algorithms for solving nonlinear equations
• MPFR
• Optimal Order of One-Point and Multipoint Iteration
• An efficient derivative free iterative method for solving systems of nonlinear equations
• A variant of Newton's method with accelerated third-order convergence

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