A family of optimal sixteenth-order multipoint methods with a linear fraction plus a trivariate polynomial as the fourth-step weighting function

DOI10.1016/j.camwa.2011.04.006zbMath1222.65046OpenAlexW2080130809MaRDI QIDQ640530

Young Ik Kim, Young Hee Geum

Publication date: 18 October 2011

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2011.04.006

zbMATH Keywords

asymptotic error constantefficiency indexoptimal ordererror equationsixteenth ordertrivariate

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05)

Related Items (15)

Full linear multistep methods as root-finders ⋮ An efficient optimal family of sixteenth order methods for nonlinear models ⋮ Simply constructed family of a Ostrowski's method with optimal order of convergence ⋮ On the construction of some tri-parametric iterative methods with memory ⋮ Higher Order Two-Point Efficient Family of Halley Type Methods for Simple Roots ⋮ Computing simple roots by an optimal sixteenth-order class ⋮ On a 4-point sixteenth-order King family of iterative methods for solving nonlinear equations ⋮ A new class of optimal four-point methods with convergence order 16 for solving nonlinear equations ⋮ A general class of one-parametric with memory method for solving nonlinear equations ⋮ Some novel and optimal families of King's method with eighth and sixteenth-order of convergence ⋮ On a general class of optimal order multipoint methods for solving nonlinear equations ⋮ Efficient methods of optimal eighth and sixteenth order convergence for solving nonlinear equations ⋮ Efficient optimal families of higher-order iterative methods with local convergence ⋮ Efficient Ostrowski-like methods of optimal eighth and sixteenth order convergence and their dynamics ⋮ Sixteenth-order optimal iterative scheme based on inverse interpolatory rational function for nonlinear equations

Uses Software

• Mathematica

Cites Work

• A multi-parameter family of three-step eighth-order iterative methods locating a simple root
• Eighth-order methods with high efficiency index for solving nonlinear equations
• Modified Ostrowski's method with eighth-order convergence and high efficiency index
• Three-step iterative methods with eighth-order convergence for solving nonlinear equations
• A new family of eighth-order iterative methods for solving nonlinear equations
• On a General Class of Multipoint Root-Finding Methods of High Computational Efficiency
• On a family of multipoint methods for non-linear equations
• Optimal Order of One-Point and Multipoint Iteration
• Some Fourth Order Multipoint Iterative Methods for Solving Equations
• A Family of Fourth Order Methods for Nonlinear Equations
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