A class of iterative methods with third-order convergence to solve nonlinear equations

DOI10.1016/j.cam.2007.02.001zbMath1143.65041OpenAlexW2106706679MaRDI QIDQ932716

Mehmet Çetin Koçak

Publication date: 11 July 2008

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

Full work available at URL: https://doi.org/10.1016/j.cam.2007.02.001

zbMATH Keywords

simulationNewton's methodnumerical examplesconvergence accelerationChebyshev methodHalley's methoditerative methodsnonlinear equationsconvergence orderfixed-point iterationsalgebraic equation solversdirect substitutionpartial substitution

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05)

Related Items (3)

A novel cubically convergent iterative method for computing complex roots of nonlinear equations ⋮ Third-order iterative methods with applications to Hammerstein equations: a unified approach ⋮ Simple geometry facilitates iterative solution of a nonlinear equation via a special transformation to accelerate convergence to third order

Cites Work

• A family of third-order methods to solve nonlinear equations by quadratic curves approximation
• Generation of root finding algorithms via perturbation theory and some formulas
• Simple geometry facilitates iterative solution of a nonlinear equation via a special transformation to accelerate convergence to third order
• Accelerated convergence in Newton's method for approximating square roots
• An acceleration of iterative processes for solving nonlinear equations
• On Halley's Iteration Method
• Accelerated Convergence in Newton’s Method
• A variant of Newton's method with accelerated third-order convergence
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