Method for finding multiple roots of polynomials

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Abstract

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 fast 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. © 2006 Elsevier Ltd. All rights reserved.

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Yan, C. D., & Chieng, W. H. (2006). Method for finding multiple roots of polynomials. Computers and Mathematics with Applications, 51(3–4), 605–620. https://doi.org/10.1016/j.camwa.2005.07.018

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