Accelerated convergence in Newton's method
SIAM Review
Numerical analysis: an introduction
Numerical analysis: an introduction
Geometric constructions of iterative functions to solve nonlinear equations
Journal of Computational and Applied Mathematics
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Letter to the Editor: Third-order modification of Newton's method
Journal of Computational and Applied Mathematics
On Newton-type methods with cubic convergence
Journal of Computational and Applied Mathematics
A new modified secant-like method for solving nonlinear equations
Computers & Mathematics with Applications
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In this paper, a new method for solving nonlinear equations f(x)=0 is presented. Analysis of the convergence shows that the asymptotic convergence order of this method is 1+3. Some numerical results are given to demonstrate its efficiency.