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Calculus of \(n\)th roots and third order iterative methods.

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Publication:1875314
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DOI10.1016/S0362-546X(01)00408-4zbMath1042.65523MaRDI QIDQ1875314

José Manuel Gutiérrez Jimenez, M. A. Salanova, Miguel A. Hernández

Publication date: 26 August 2004

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)



Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05)


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New methods for approximating square roots ⋮ Inverse function, Taylor's expansion and extended Schröder's processes ⋮ High order algorithms for approximatingnth roots ⋮ Geometric constructions of iterative functions to solve nonlinear equations ⋮ Convergence regions for the Chebyshev-Halley family ⋮ A numerical method for computing the principal square root of a matrix ⋮ Some variants of the Chebyshev–Halley family of methods with fifth order of convergence ⋮ Accelerated convergence in Newton's method for approximating square roots ⋮ Example for equivalence of dual and information-based optimal control ⋮ Newton's method and high-order algorithms for the \(n\)th root computation



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