The convergence theorem for a family deformed Chebyshev method in Banach space

DOI10.1016/j.amc.2006.05.022zbMath1151.65051OpenAlexW1966660852MaRDI QIDQ858802

Yueqing Zhao, Qing-Biao Wu

Publication date: 11 January 2007

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

Full work available at URL: https://doi.org/10.1016/j.amc.2006.05.022

zbMATH Keywords

convergenceChebyshev methodBanach spacenonlinear operator equation

Mathematics Subject Classification ID

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

Related Items (9)

Convergence of a continuation method under majorant conditions ⋮ On Chebyshev‐type methods free from second derivative ⋮ Sixth order derivative free family of iterative methods ⋮ Derivative free algorithm for solving nonlinear equations ⋮ Analysis of convergence for improved Chebyshev-Halley methods under different conditions ⋮ A new semilocal convergence theorem of Müller's method ⋮ Constructing third-order derivative-free iterative methods ⋮ Convergence of a continuation method under Lipschitz continuous derivative in Banach spaces ⋮ Fourth-order convergence theorem by using majorizing functions for super-Halley method in Banach spaces

Cites Work

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• Chebyshev method and convexity
• Convergence on the iteration of Halley family in weak conditions
• Third-order iterative methods for operators with bounded second derivative
• New recurrence relations for Chebyshev method
• A fast Chebyshev's method for quadratic equations.
• Second-derivative-free variant of the Chebyshev method for nonlinear equations
• Results on the Chebyshev method in banach spaces
• Modification of the Kantorovich assumptions for semilocal convergence of the Chebyshev method

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