Kepler equation and accelerated Newton method
Journal of Computational and Applied Mathematics
Some variant of Newton's method with third-order convergence
Applied Mathematics and Computation
The Mathematica Book
Geometric constructions of iterative functions to solve nonlinear equations
Journal of Computational and Applied Mathematics
A modified Newton method with cubic convergence: the multivariate case
Journal of Computational and Applied Mathematics
MPFR: A multiple-precision binary floating-point library with correct rounding
ACM Transactions on Mathematical Software (TOMS)
Some iterative methods for solving a system of nonlinear equations
Computers & Mathematics with Applications
Remarks on “On a General Class of Multipoint Root-Finding Methods of High Computational Efficiency”
SIAM Journal on Numerical Analysis
An efficient fourth order weighted-Newton method for systems of nonlinear equations
Numerical Algorithms
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In this paper, we present a three-step iterative method of convergence order five for solving systems of nonlinear equations. The methodology is based on the two-step Homeier's method with cubic convergence (Homeier, 2004). Computational efficiency in its general form is discussed and a comparison between the efficiency of proposed technique and existing ones is made. The performance is tested through numerical examples. Moreover, theoretical results concerning order of convergence and computational efficiency are verified in the examples. It is shown that the present method has an edge over existing methods, particularly when applied to large systems of equations.