Extended sufficient semilocal convergence for the secant method

DOI10.1016/j.camwa.2011.05.040zbMath1228.65083OpenAlexW2086709614MaRDI QIDQ651533

Ioannis K. Argyros, Saïd Hilout, Yeol Je Cho

Publication date: 18 December 2011

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2011.05.040

zbMATH Keywords

semilocal convergenceBanach spacesecant methoddivided differencemajorizing sequencerecurrent functions

Mathematics Subject Classification ID

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

Cites Work

• General local convergence theory for a class of iterative processes and its applications to Newton's method
• A convergence theorem for Newton-like methods in Banach spaces
• Extended iterative methods for the solution of operator equations
• Untere Fehlerschranken für Regula-Falsi-Verfahren
• On the Newton-Kantorovich hypothesis for solving equations
• A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space
• Secant-like methods for solving nonlinear integral equations of the Hammerstein type
• A multipoint method of third order
• Solving a special case of conservative problems by secant-like methods
• New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems
• Convergence conditions for secant-type methods
• On an iterative algorithm of order 1.839… for solving nonlinear operator equations^∗)
• New sufficient convergence conditions for the secant method
• Convergence and Applications of Newton-type Iterations
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