Computing simple roots by an optimal sixteenth-order class

DOI10.1155/2012/958020zbMath1268.65070OpenAlexW2046035725WikidataQ58907005 ScholiaQ58907005MaRDI QIDQ1953001

Fazlollah Soleymani, H. Salmani, Stanford Shateyi

Publication date: 3 June 2013

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

Full work available at URL: https://doi.org/10.1155/2012/958020

zbMATH Keywords

numerical resultssimple zerosefficiency indexerror equationinterval Newton's methodfour-step cycleoptimal 16th order classoptimal three-step derivative-involved method

Mathematics Subject Classification ID

Interval and finite arithmetic (65G30) Numerical computation of solutions to single equations (65H05)

Related Items (7)

A two-parameter family of fourth-order iterative methods with optimal convergence for multiple zeros ⋮ Some optimal iterative methods and their with memory variants ⋮ On a numerical technique for finding multiple zeros and its dynamic ⋮ A new class of Halley's method with third-order convergence for solving nonlinear equations ⋮ A novel iterative method for polar decomposition and matrix sign function ⋮ Two-point generalized Hermite interpolation: double-weight function and functional recursion methods for solving nonlinear equations ⋮ An optimal thirty-second-order iterative method for solving nonlinear equations and a conjecture

Uses Software

• Mathematica

Cites Work

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• An optimized derivative-free form of the Potra-Pták method
• On a new method for computing the numerical solution of systems of nonlinear equations
• A biparametric family of optimally convergent sixteenth-order multipoint methods with their fourth-step weighting function as a sum of a rational and a generic two-variable function
• Enriched contact finite elements for stable peeling computations
• On novel classes of iterative methods for solving nonlinear equations
• Optimal Order of One-Point and Multipoint Iteration
• A new family of modified Ostrowski's methods with accelerated eighth order convergence

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