Convergence by nondiscrete mathematical induction of a two step secant's method

DOI10.1216/rmjm/1181068756zbMath1140.65040OpenAlexW2033118611MaRDI QIDQ2477966

Sergio Amat, J. Gretay, Concepción Bermúdez, Sonia Busquier

Publication date: 14 March 2008

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmjm/1181068756

zbMATH Keywords

algorithmiterative methodsBanach spacenonlinear operator equationssemi-local convergencenondiscrete mathematical inductiontwo-step secant's iterative schemetwo-step Steffensen's method

Mathematics Subject Classification ID

Newton-type methods (49M15) Iterative procedures involving nonlinear operators (47J25) Numerical solutions to equations with nonlinear operators (65J15)

Related Items

A semilocal convergence for a uniparametric family of efficient secant-like methods, Secant-type methods and nondiscrete induction, Majorizing sequences for Newton's method under centred conditions for the derivative, Extending the applicability of Newton’s method using nondiscrete induction

Cites Work

• Newton-like methods for the computation of fixed points
• A generalization of regula falsi
• On a higher order secant method.
• A class of quasi-Newton generalized Steffensen methods on 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
• Convergence and numerical analysis of a family of two-step Steffensen's methods
• Some metric aspects of the open mapping and closed graph theorems
• Nondiscrete induction and double step secant method.
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