Point Estimation of Cubically Convergent Root Finding Method of Weierstrass’ Type
نویسنده
چکیده
The aim of this paper is to state initial conditions for the safe and fast convergence of the simultaneous method of Weierstrass’ type for finding simple zeros of algebraic polynomial. This conditions are computationally verifiable and they depend only on the available data polynomial coefficients, its degree and initial approximations z 1 , . . . , z (0) n to the zeros. It is shown that under the stated conditions, the proposed iterative method is convergent.
منابع مشابه
A Family of Root Finding Methods*
A one parameter family of iteration functions for finding roots is derived. ] h e family includes the Laguerre, Halley, Ostrowski and Euler methods and, as a limiting case, Newton's method. All the methods of the family are cubically convergent for a simple root (except Newton's which is quadratically convergent). The superior behavior of Laguerre's method, when starting from a point z for whic...
متن کاملA cubically convergent class of root finding iterative methods
In this paper, we propose a new two-parameter class of iterative methods to solve a nonlinear equation. It is proved that any method in this class is cubically convergent if and only if the parameters sum up to one. Some of the existing third-order methods, by suitable selection of parameters, can be put in this class. Every iteration of the class requires an evaluation of the function, three o...
متن کاملOn a Cubically Convergent Iterative Method for Matrix Sign
We propose an iterative method for finding matrix sign function. It is shown that the scheme has global behavior with cubical rate of convergence. Examples are included to show the applicability and efficiency of the proposed scheme and its reciprocal.
متن کاملA Family of Cubically Convergent Methods for Solving Nonlinear Equations
Ujević et al. introduced a family of methods for solving nonlinear equations in [7]. For certain choices of parameters, firstly, they showed that the classical Newton’s method is a member of this family and their methods are better than classical Newton’s method. Then they introduced a particular method. However, in most cases, their efficiency is worse than classical Newton’s method. This is t...
متن کاملOn a family of Weierstrass-type root-finding methods with high order of convergence
in English: In 1985, Kyurkchiev and Andreev [1] constructed a sequence of iterative methods for finding all zeros of a polynomial simultaneously. In the literature there are only local convergence results for these methods (see [1, 5]). In this talk, we present a semilocal convergence theorem for Kyurkchiev-Andreev’s methods under computationally verifiable initial conditions and with an a post...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014