A Family of Optimal Multipoint Root-Finding Methods Based on the Interpolating Polynomials
نویسنده
چکیده
A family of simple derivative-free multipoint iterative methods, based on the interpolating polynomials, for solving nonlinear equations is presented. It is shown that the presented n-point iterative method has the convergence order 2n−1 with n function evaluations per iteration. It is an optimal iterative method in the sense of the Kung-Traub’s conjecture. Numerical examples are included to support the result of theoretical convergence analysis and demonstrate efficiency of the proposed method.
منابع مشابه
An Efficient Family of Root-Finding Methods with Optimal Eighth-Order Convergence
We derive a family of eighth-order multipoint methods for the solution of nonlinear equations. In terms of computational cost, the family requires evaluations of only three functions and one first derivative per iteration. This implies that the efficiency index of the present methods is 1.682. Kung and Traub 1974 conjectured that multipoint iteration methods without memory based on n evaluation...
متن کاملAn Optimal Biparametric Multipoint Family and Its Self-Acceleration with Memory for Solving Nonlinear Equations
In this paper, a family of Steffensen-type methods of optimal order of convergence with two parameters is constructed by direct Newtonian interpolation. It satisfies the conjecture proposed by Kung and Traub (J. Assoc. Comput. Math. 1974, 21, 634–651) that an iterative method based on m evaluations per iteration without memory would arrive at the optimal convergence of order 2m−1. Furthermore, ...
متن کاملSolution of Bang-Bang Optimal Control Problems by Using Bezier Polynomials
In this paper, a new numerical method is presented for solving the optimal control problems of Bang-Bang type with free or fixed terminal time. The method is based on Bezier polynomials which are presented in any interval as $[t_0,t_f]$. The problems are reduced to a constrained problems which can be solved by using Lagrangian method. The constraints of these problems are terminal state and con...
متن کاملA New Family of Multipoint Iterative Methods for Finding Multiple Roots of Nonlinear Equations
In this paper, we present a new family of multipoint iterative methods for finding multip le zeros of nonlinear equations. Per iterat ion the new method requires three evaluations of functions and one of its first derivative. We have analysed and proved the order of convergence of the new methods. Finally, the numerical examples demonstrate that the proposed methods are superior to the existing...
متن کاملA spectral method based on the second kind Chebyshev polynomials for solving a class of fractional optimal control problems
In this paper, we consider the second-kind Chebyshev polynomials (SKCPs) for the numerical solution of the fractional optimal control problems (FOCPs). Firstly, an introduction of the fractional calculus and properties of the shifted SKCPs are given and then operational matrix of fractional integration is introduced. Next, these properties are used together with the Legendre-Gauss quadrature fo...
متن کامل