On the generalization of secant method and the order of convergence

DOI10.11948/20240082zbMATH Open1548.6512MaRDI QIDQ6617558

J. C. Trillo, Pedro J. Martínez-Aparacio, V. Candela, Natalia Expósito

Publication date: 11 October 2024

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

zbMATH Keywords

nonlinear equationsorder of convergencesecant methodMüller method

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05) Rate of convergence, degree of approximation (41A25)

Cites Work

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• Topological properties of the immediate basins of attraction for the secant method
• A generalization of Müller's iteration method based on standard information
• Secant-like methods for solving nonlinear models with applications to chemistry
• A class of third order iterative Kurchatov-Steffensen (derivative free) methods for solving nonlinear equations
• An augmented memoryless BFGS method based on a modified secant equation with application to compressed sensing
• Achieving an extended convergence analysis for the secant method under a restricted Hölder continuity condition
• Convergence and dynamics of improved Chebyshev-secant-type methods for non differentiable operators
• Perturbation bounds for polynomials
• Improved convergence analysis of the Secant method using restricted convergence domains with real-world applications
• Improved convergence ball and error analysis of Müller's method
• A family of global convergent inexact secant methods for nonconvex constrained optimization

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