An optimal multiple root-finding method of order three
Journal of Computational and Applied Mathematics
A modified Newton method for rootfinding with cubic convergence
Journal of Computational and Applied Mathematics
High-order nonlinear solver for multiple roots
Computers & Mathematics with Applications
Three-step iterative methods with eighth-order convergence for solving nonlinear equations
Journal of Computational and Applied Mathematics
Some fourth-order nonlinear solvers with closed formulae for multiple roots
Computers & Mathematics with Applications
Accelerating generators of iterative methods for finding multiple roots of nonlinear equations
Computers & Mathematics with Applications
Extension of Murakami's high-order non-linear solver to multiple roots
International Journal of Computer Mathematics
Letter to the editor: New higher order methods for solving nonlinear equations with multiple roots
Journal of Computational and Applied Mathematics
On a General Class of Multipoint Root-Finding Methods of High Computational Efficiency
SIAM Journal on Numerical Analysis
Second-derivative free methods of third and fourth order for solving nonlinear equations
International Journal of Computer Mathematics
A fourth-order derivative-free algorithm for nonlinear equations
Journal of Computational and Applied Mathematics
Three-step iterative methods with optimal eighth-order convergence
Journal of Computational and Applied Mathematics
On the new fourth-order methods for the simultaneous approximation of polynomial zeros
Journal of Computational and Applied Mathematics
On efficient two-parameter methods for solving nonlinear equations
Numerical Algorithms
| Hi-index | 7.29 |
In this paper we consider a nonlinear equation f(x)=0 having finitely many roots in a bounded interval. Based on the so-called numerical integration method [B.I. Yun, A non-iterative method for solving non-linear equations, Appl. Math. Comput. 198 (2008) 691-699] without any initial guess, we propose iterative methods to obtain all the roots of the nonlinear equation. In the result, an algorithm to find all of the simple roots and multiple ones as well as the extrema of f(x) is developed. Moreover, criteria for distinguishing zeros and extrema are included in the algorithm. Availability of the proposed method is demonstrated by some numerical examples.