A family of higher order derivative free methods for nonlinear systems with local convergence analysis

DOI10.1007/s40314-018-0663-xzbMath1413.65200OpenAlexW2808532770MaRDI QIDQ1715648

Erdal Karapınar

Publication date: 29 January 2019

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

Full work available at URL: https://doi.org/10.1007/s40314-018-0663-x

zbMATH Keywords

system of nonlinear equationscomputational efficiencyorder of convergenceSteffensen's methodderivative free methods

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 (2)

Higher order Jarratt-like iterations for solving systems of nonlinear equations ⋮ Optimal choice of parameters in higher-order derivative-free iterative methods for systems of nonlinear equations

Uses Software

• Mathematica
• MPFR

Cites Work

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• Ostrowski type methods for solving systems of nonlinear equations
• On the approximation of derivatives using divided difference operators preserving the local convergence order of iterative methods
• A novel derivative free algorithm with seventh order convergence for solving systems of nonlinear equations
• Frozen divided difference scheme for solving systems of nonlinear equations
• A family of iterative methods that uses divided differences of first and second orders
• Dynamics of the King and Jarratt iterations
• On the local convergence of a family of two-step iterative methods for solving nonlinear equations
• Local convergence for multi-point-parametric Chebyshev-Halley-type methods of high convergence order
• Chaotic dynamics of a third-order Newton-type method
• A modified Chebyshev's iterative method with at least sixth order of convergence
• Accelerated iterative methods for finding solutions of a system of nonlinear equations
• New iterations of \(R\)-order four with reduced computational cost
• Optimal equi-scaled families of Jarratt's method
• Computational Methods in Nonlinear Analysis
• Remarks on “On a General Class of Multipoint Root-Finding Methods of High Computational Efficiency”
• Convergence and Applications of Newton-type Iterations
• MPFR
• Solving Nonlinear Equations with Newton's Method
• An efficient derivative free iterative method for solving systems of nonlinear equations

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