Accelerated convergence in Newton's method for approximating square roots

DOI10.1016/j.cam.2004.09.025zbMath1062.65051OpenAlexW1994473530MaRDI QIDQ1763772

Xianqiang Yang

Publication date: 22 February 2005

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

Full work available at URL: https://doi.org/10.1016/j.cam.2004.09.025

zbMATH Keywords

Newton's methodnumerical examplesconvergence accelerationSquare rootIterative processes

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05)

Related Items

New methods for approximating square roots ⋮ Inverse function, Taylor's expansion and extended Schröder's processes ⋮ A note on machine method for root extraction ⋮ A class of iterative methods with third-order convergence to solve nonlinear equations ⋮ On exponential convergence of nonlinear gradient dynamics system with application to square root finding ⋮ Some variants of Cauchy's method with accelerated fourth-order convergence ⋮ New identities in the Catalan triangle ⋮ Methods with prefixed order for approximating square roots with global and general convergence

Cites Work

• Indices of convexity and concavity. Application to Halley method
• \(n\)th root extraction: Double iteration process and Newton's method
• Calculus of \(n\)th roots and third order iterative methods.
• Algorithms for \(n\)-th root approximation.
• On Halley's Iteration Method
• Accelerated Convergence in Newton’s Method
• A family of Chebyshev-Halley type methods in Banach spaces
• On a new Newton-Mysovskii-type theorem with applications to inexact Newton-like methods and their discretizations

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