High Order Fixed Point and Newton’s Methods in Banach Space

DOI10.1080/01630563.2021.1873365zbMath1468.65063OpenAlexW3123520908MaRDI QIDQ4985184

François Dubeau

Publication date: 22 April 2021

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630563.2021.1873365

zbMATH Keywords

Newton's methodBanach spacenecessary conditionssufficient conditionsfixed point methodTaylor's expansionhigher order convergence

Mathematics Subject Classification ID

Numerical solutions to equations with nonlinear operators (65J15)

Cites Work

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• \(p\)th-order numerical methods for solving systems of nonlinear equations
• On the rediscovery of Halley's iterative method for computing the zero of an analytic function
• Computational implementation of the multivariate Halley method for solving nonlinear systems of equations
• Convergence and Applications of Newton-type Iterations
• A family of Chebyshev-Halley type methods in Banach spaces
• An acceleration of Newton's method: Super-Halley method

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