Improved convergence analysis for the Secant method based on a certain type of recurrence relations

DOI10.1080/00207160410001688600zbMath1060.65058OpenAlexW2071995418MaRDI QIDQ4831425

Ioannis K. Argyros

Publication date: 29 December 2004

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160410001688600

zbMATH Keywords

convergenceerror boundsBanach spacenonlinear operator equationsecant method

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (3)

A weak condition for secant method to solve systems of nonlinear equations ⋮ Convergence analysis for the secant method based on new recurrence relations ⋮ Toward a unified theory for third \(R\)-order iterative methods for operators with unbounded second derivative

Cites Work

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• A convergence theorem for Newton-like methods in Banach spaces
• Semilocal convergence of the secant method under mild convergence conditions of differentiability
• Secant-like methods for solving nonlinear integral equations of the Hammerstein type
• A new type of recurrence relations for the secant method^∗

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