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Method for finding multiple roots of polynomials

✍ Scribed by Chang-Dau Yan; Wei-Hua Chieng

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
851 KB
Volume
51
Category
Article
ISSN
0898-1221

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✦ Synopsis

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.

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