On the Generalized Halley Method for Solving Nonlinear Equations
نویسنده
چکیده
Halley’s method is a famous iteration method for solving nonlinear equations F (X) = 0. Some Kantorovich-like theorems have been given, including extensions for general spaces. Quasi-Halley methods were proposed too. This paper uses the generalized inverse approach in order to obtain a robust generalized Halley method.
منابع مشابه
A modification of Chebyshev-Halley method free from second derivatives for nonlinear equations
In this paper, we present a new modification of Chebyshev-Halley method, free from second derivatives, to solve nonlinear equations. The convergence analysis shows that our modification is third-order convergent. Every iteration of this method requires one function and two first derivative evaluations. So, its efficiency index is $3^{1/3}=1.442$ that is better than that o...
متن کاملThe smoothed particle hydrodynamics method for solving generalized variable coefficient Schrodinger equation and Schrodinger-Boussinesq system
A meshless numerical technique is proposed for solving the generalized variable coefficient Schrodinger equation and Schrodinger-Boussinesq system with electromagnetic fields. The employed meshless technique is based on a generalized smoothed particle hydrodynamics (SPH) approach. The spatial direction has been discretized with the generalized SPH technique. Thus, we obtain a system of ordinary...
متن کاملSolving infinite system of nonlinear integral equations by using F-generalized Meir-Keeler condensing operators, measure of noncompactness and modified homotopy perturbation.
In this article to prove existence of solution of infinite system of nonlinear integral equations, we consider the space of solution containing all convergence sequences with a finite limit, as with a suitable norm is a Banach space. By creating a generalization of Meir-Keeler condensing operators which is named as F-generalized Meir-Keeler condensing operators and measure of noncompactness, we...
متن کاملDegenerate kernel approximation method for solving Hammerstein system of Fredholm integral equations of the second kind
Degenerate kernel approximation method is generalized to solve Hammerstein system of Fredholm integral equations of the second kind. This method approximates the system of integral equations by constructing degenerate kernel approximations and then the problem is reduced to the solution of a system of algebraic equations. Convergence analysis is investigated and on some test problems, the propo...
متن کاملSome iterative methods free from second derivatives for nonlinear equations
In a recent paper, Noor [M. Aslam Noor, New classes of iterative methods for nonlinear equations, Appl. Math. Comput., 2007, doi:10.1016/j.amc:2007], suggested and analyzed a generalized one parameter Halley method for solving nonlinear equations using. In this paper, we modified this method which has fourth order convergence. As special cases, we obtain a family of third-order iterative method...
متن کامل