On a robust Aitken-Newton method based on the Hermite polynomial

DOI10.1016/j.amc.2016.03.036zbMath1410.65169OpenAlexW2412108381MaRDI QIDQ1733562

Ion Păvăloiu, Emil Cătinaş

Publication date: 21 March 2019

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

Full work available at URL: https://doi.org/10.1016/j.amc.2016.03.036

zbMATH Keywords

monotone convergenceinverse interpolationNewton-type iterative methods(sided) convergence domainsnonlinear equations in \(\mathbb{R}\)

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05)

Related Items (5)

A new optimal method of order four of Hermite-Steffensen type ⋮ Aitken based modified Kalman filtering stochastic gradient algorithm for dual-rate nonlinear models ⋮ Some stochastic gradient algorithms for Hammerstein systems with piecewise linearity ⋮ Orthogonal polynomials and Möbius transformations ⋮ The convergence of a class of parallel Newton-type iterative methods

Cites Work

• A Steffensen type method of two steps in Banach spaces with applications
• Bilateral approximations for some Aitken-Steffensen-Hermite type methods of order three
• A family of modified Ostrowski's methods with optimal eighth order of convergence
• Eighth-order methods with high efficiency index for solving nonlinear equations
• Some improvements of Ostrowski's method
• Approximation of the roots of equations by Aitken-Steffensen-type monotonic sequences
• On an Aitken-Newton type method
• Generating optimal derivative free iterative methods for nonlinear equations by using polynomial interpolation
• An improved local convergence analysis for Newton-Steffensen-type method
• Certain improvements of Chebyshev-Halley methods with accelerated fourth-order convergence
• Optimal Steffensen-type methods with eighth order of convergence
• A composite third order Newton-Steffensen method for solving nonlinear equations
• On a General Class of Multipoint Root-Finding Methods of High Computational Efficiency
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