On Enclosing Simple Roots of Nonlinear Equations

DOI10.2307/2153250zbMath0798.65062OpenAlexW4237627891MaRDI QIDQ4274393

Florian A. Potra, Yixun Shi, G. E. Alefeld

Publication date: 30 October 1994

Full work available at URL: https://doi.org/10.2307/2153250

zbMATH Keywords

interval arithmeticnonlinear equations\(R\)-order of convergenceefficiency indexenclosing method

Mathematics Subject Classification ID

Interval and finite arithmetic (65G30) Numerical computation of solutions to single equations (65H05)

Related Items (15)

Some substantial modifications and improvements for derivative-free iterative methods and derivative-free transformation for multiple zeros ⋮ An improved exponential regula falsi methods with quadratic convergence of both diameter and point for solving nonlinear equations ⋮ A modification of Muller's method ⋮ An improved regula falsi method with quadratic convergence of both diameter and point for enclosing simple zeros of nonlinear equations ⋮ On the higher-order method for the solution of a nonlinear scalar equation ⋮ Unnamed Item ⋮ Improving the efficiency index in enclosing a root of an equation ⋮ Improved Muller method and bisection method with global and asymptotic superlinear convergence of both point and interval for solving nonlinear equations ⋮ An improved class of regula falsi methods of third order for solving nonlinear equations in \(\mathbb R\) ⋮ New high-order convergence iteration methods without employing derivatives for solving nonlinear equations ⋮ An exponential regula falsi method for solving nonlinear equations ⋮ Average-Case Optimality of a Hybrid Secant-Bisection Method ⋮ A derivative free globally convergent method and its deformations ⋮ A new family of exponential iteration methods with quadratic convergence of both diameters and points for enclosing zeros of nonlinear equations ⋮ Always convergent iteration methods for nonlinear equations of Lipschitz functions

Uses Software

• BRENT

Cites Work

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• On Q-order and R-order of convergence
• Some efficient methods for enclosing simple zeros of nonlinear equations
• Methods without secant steps for finding a bracketed root
• Eingrenzung von Lösungen nichtlinearer Gleichungen durch Verfahren mit höherer Konvergenzgeschwindigkeit. (Inclusion of solutions of nonlinear equations by methods with higher convergence rate).
• An efficient derivative-free method for solving nonlinear equations
• On Two Higher Order Enclosing Methods of J. W. Schmidt
• Three New Rapidly Convergent Algorithms for Finding a Zero of a Function
• A new high order method of regula falsi type for computing a root of an equation

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