Practical quasi-Newton methods for solving nonlinear systems
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
An acceleration of Newton's method: Super-Halley method
Applied Mathematics and Computation
Geometric constructions of iterative functions to solve nonlinear equations
Journal of Computational and Applied Mathematics
A modified Newton method for rootfinding with cubic convergence
Journal of Computational and Applied Mathematics
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Hi-index | 0.00 |
We derive a one-parameter family of second-order methods for solving f(x)=0. The approximation process is carried out by fitting the model m(x)=epx(ax+b) to the function f(x) and its derivative f'(x) at a point xi and solving m(x)=0. Numerical examples show that the method works when Newton's method fails. A composite method with cubic convergence, based on the new scheme, is also presented. Error analysis providing the order of convergence is given. Theoretical comparisons of computational efficiency are made and some rules to assist in the selection of an iteration formula are derived.