Numerical analysis: an introduction
Numerical analysis: an introduction
Some variant of Newton's method with third-order convergence
Applied Mathematics and Computation
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
On Newton-type methods with cubic convergence
Journal of Computational and Applied Mathematics
Letter to the Editor: Third-order modification of Newton's method
Journal of Computational and Applied Mathematics
Some modifications of Newton's method with fifth-order convergence
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Fourth-order two-step iterative methods for determining multiple zeros of non-linear equations
International Journal of Computer Mathematics
Modified Newton's method for systems of nonlinear equations with singular Jacobian
Journal of Computational and Applied Mathematics
International Journal of Computer Mathematics
New families of nonlinear third-order solvers for finding multiple roots
Computers & Mathematics with Applications
On Newton-type methods for multiple roots with cubic convergence
Journal of Computational and Applied Mathematics
On Newton-type methods with cubic convergence
Journal of Computational and Applied Mathematics
Accelerating generators of iterative methods for finding multiple roots of nonlinear equations
Computers & Mathematics with Applications
Accurate fourteenth-order methods for solving nonlinear equations
Numerical Algorithms
Hi-index | 7.30 |
In recent papers (Appl. Math. Comput. 140 (2003) 419-426; Appl. Math. Lett. 13 (2000) 87-93) a new modification of the Newton's method (mNm) which produces iterative methods with order of convergence three have been proposed. Here we study the order of convergence of such methods when we have multiple roots. We prove that the order of convergence of the mNm go down to one but, when the multiplicity p is known, it may be rised up to two by using two different types of correction. When p is unknown we show that the two most efficient methods in the family of the mNm converge faster than the classical Newton's method.