Always convergent iteration methods for nonlinear equations of Lipschitz functions

DOI10.1007/s11075-014-9905-1zbMath1319.65036OpenAlexW2013734933MaRDI QIDQ2351494

Aurel Galantai, Jozsef Abaffy

Publication date: 23 June 2015

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

Full work available at URL: https://doi.org/10.1007/s11075-014-9905-1

zbMATH Keywords

numerical examplesnonlinear equationmonotone convergenceiteration methodsLipschitz functionsconvergence speed

Mathematics Subject Classification ID

Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Numerical computation of solutions to single equations (65H05)

Related Items (4)

Always convergent methods for nonlinear equations of several variables ⋮ Backward step control for Hilbert space problems ⋮ Backward Step Control for Global Newton-Type Methods ⋮ Always convergent iteration methods for nonlinear equations of Lipschitz functions

Uses Software

• RROOT_748
• Algorithm 748
• zeroin

Cites Work

• Univariate geometric Lipschitz global optimization algorithms
• A study of accelerated Newton methods for multiple polynomial roots
• Some efficient methods for enclosing simple zeros of nonlinear equations
• Globally convergent algorithm for solving nonlinear equations
• Always convergent iteration methods for nonlinear equations of Lipschitz functions
• Eingrenzung von Lösungen nichtlinearer Gleichungen durch Verfahren mit höherer Konvergenzgeschwindigkeit. (Inclusion of solutions of nonlinear equations by methods with higher convergence rate).
• A globally convergent method for solving nonlinear equations without the differentiability condition
• An efficient derivative-free method for solving nonlinear equations
• Automatic Selection of Sequence Transformations
• Two Efficient Algorithms with Guaranteed Convergence for Finding a Zero of a Function
• On Enclosing Simple Roots of Nonlinear Equations
• Algorithm 748: enclosing zeros of continuous functions
• Finding the minimal root of an equation with the multiextremal and nondifferentiable left-hand part
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