A novel derivative free algorithm with seventh order convergence for solving systems of nonlinear equations

DOI10.1007/s11075-014-9832-1zbMath1320.65077OpenAlexW1995753230MaRDI QIDQ478204

Janak Raj Sharma, Himani Arora

Publication date: 3 December 2014

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-014-9832-1

zbMATH Keywords

algorithmnumerical examplesystems of nonlinear equationscomputational efficiencyorder of convergencederivative-free methodsseventh-order iterative method

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Complexity and performance of numerical algorithms (65Y20) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58)

Related Items (18)

Extended ball convergence for a seventh order derivative free class of algorithms for nonlinear equations ⋮ Highly efficient family of iterative methods for solving nonlinear models ⋮ On the convergence of a novel seventh convergence order schemes for solving equations ⋮ New efficient derivative free family of seventh-order methods for solving systems of nonlinear equations ⋮ A study of the local convergence of a derivative free method in Banach spaces ⋮ Optimal choice of parameters in higher-order derivative-free iterative methods for systems of nonlinear equations ⋮ A study of the local convergence of a fifth order iterative method ⋮ An adaptive Steffensen-like families for solving nonlinear systems using frozen divided differences ⋮ A family of higher order derivative free methods for nonlinear systems with local convergence analysis ⋮ Stable high-order iterative methods for solving nonlinear models ⋮ General efficient class of Steffensen type methods with memory for solving systems of nonlinear equations ⋮ Multi-step derivative-free preconditioned Newton method for solving systems of nonlinear equations ⋮ Generalized Kung-Traub method and its multi-step iteration in Banach spaces ⋮ Higher-order modification of Steffensen's method for solving system of nonlinear equations ⋮ ON A CLASS OF EFFICIENT HIGHER ORDER NEWTON-LIKE METHODS ⋮ Some higher-order iteration functions for solving nonlinear models ⋮ A simple yet efficient derivative free family of seventh order methods for systems of nonlinear equations ⋮ Highly efficient solvers for nonlinear equations in Banach space

Uses Software

• Mathematica
• MPFR

Cites Work

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• A technique to choose the most efficient method between secant method and some variants
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• Frozen divided difference scheme for solving systems of nonlinear equations
• A variant of Steffensen's method of fourth-order convergence and its applications
• A class of two-step Steffensen type methods with fourth-order convergence
• A family of Steffensen type methods with seventh-order convergence
• Accelerated iterative methods for finding solutions of a system of nonlinear equations
• Analysis of two Chebyshev-like third order methods free from second derivatives for solving systems of nonlinear equations
• Remarks on “On a General Class of Multipoint Root-Finding Methods of High Computational Efficiency”
• MPFR
• Solving Nonlinear Equations with Newton's Method
• A note on \(Q\)-order of convergence
• A modified Newton-Jarratt's composition

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