標題: Method for finding multiple roots of polynomials
作者: Yan, CD
Chieng, WH
機械工程學系
Department of Mechanical Engineering
關鍵字: multiple root;root finding;zero finding;polynomial GCD;approximate divisibility;approximate GCD
公開日期: 1-二月-2006
摘要: Conventional numerical methods for finding multiple roots of polynomials are inaccurate. The accuracy is unsatisfactory because the derivatives of the polynomial in the intermediate steps of the associated root-finding procedures are eliminated. Engineering applications require that this problem be solved. This work presents an easy-to-implement method that theoretically completely resolves the multiple-root issue. The proposed method adopts the Euclidean algorithm to obtain the greatest common divisor (GCD) of a polynomial and its first derivative. The GCD may be approximate because of computational inaccuracy. The multiple roots are then deflated into simple ones and then determined by conventional root-finding methods. The multiplicities of the roots are accordingly calculated. A detailed derivation and test examples are provided to demonstrate the efficiency of this method. (c) 2006 Elsevier Ltd. All rights reserved.
URI: http://dx.doi.org/10.1016/j.camwa.2005.07.018
http://hdl.handle.net/11536/12689
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2005.07.018
期刊: COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume: 51
Issue: 3-4
起始頁: 605
結束頁: 620
顯示於類別:期刊論文


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