On an efficient inclusion method for finding polynomial zeros

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:290

Article

Milosevic, Dusan M.¹  Milosevic, Mimica R.²  Dzunic, Jovana¹ 

[1] Univ Nis, Fac Elect Engn, Nish 18000, Serbia

[2] Univ Union Nikola Testa, Fac Management Civil Engn, Belgrade 11000, Serbia

关键词: Polynomial zeros;    Simultaneous methods;    Inclusion methods;    Convergence conditions;    Circular interval arithmetic;   

DOI  :  10.1016/j.cam.2015.05.015

来源: Elsevier

【 摘 要 】

New efficient iterative method of Halley's type for the simultaneous inclusion of all simple complex zeros of a polynomial is proposed. The presented convergence analysis, which uses the concept of the R-order of convergence of mutually dependent sequences, shows that the convergence rate of the basic fourth order method is increased from 4 to 9 using a two-point correction. The proposed inclusion method possesses high computational efficiency since the increase of convergence is attained with only one additional function evaluation per sought zero. Further acceleration of the proposed method is carried out using the Gauss-Seidel procedure. Some computational aspects and three numerical examples are given in order to demonstrate high computational efficiency and the convergence properties of the proposed methods. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

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