Some modifications of Newton's method with higher-order convergence for solving nonlinear equations

DOI10.1016/j.cam.2008.09.023zbMath1168.65344OpenAlexW2019772791MaRDI QIDQ1019800

Liang Fang, Guo-Ping He

Publication date: 28 May 2009

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

Full work available at URL: https://doi.org/10.1016/j.cam.2008.09.023

zbMATH Keywords

Newton's methoditerative methodnonlinear equationsorder of convergencemulti-step iterative method

Mathematics Subject Classification ID

Numerical computation of solutions to single equations (65H05) Rate of convergence, degree of approximation (41A25) Numerical quadrature and cubature formulas (65D32)

Related Items (9)

Sixteenth-order method for nonlinear equations ⋮ Computing eigenpairs in augmented Krylov subspace produced by Jacobi-Davidson correction equation ⋮ An efficient and straightforward numerical technique coupled to classical Newton's method for enhancing the accuracy of approximate solutions associated with scalar nonlinear equations ⋮ Some modifications of the quasilinearization method with higher-order convergence for solving nonlinear BVPs ⋮ A novel cubically convergent iterative method for computing complex roots of nonlinear equations ⋮ A fourth-order derivative-free algorithm for nonlinear equations ⋮ Modifications of higher-order convergence for solving nonlinear equations ⋮ The simple finite volume Lax-Wendroff weighted essentially nonoscillatory schemes for shallow water equations with bottom topography ⋮ A new smoothing method for solving nonlinear complementarity problems

Uses Software

• LAPACK
• NITSOL
• PETSc
• LINPACK
• LSODE
• KELLEY
• HOMPACK

Cites Work

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• Modified iterative methods with cubic convergence for solving nonlinear equations
• A cubically convergent Newton-type method under weak conditions
• Some higher-order modifications of Newton's method for solving nonlinear equations
• A modified Newton method for rootfinding with cubic convergence.
• A variant of Cauchy's method with accelerated fifth-order convergence.
• The improvements of modified Newton's method
• Some second-derivative-free variants of super-Halley method with fourth-order convergence
• A composite third order Newton-Steffensen method for solving nonlinear equations
• A family of methods for solving nonlinear equations

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