Method for finding multiple roots of polynomials

Authors:
Chang-Dau Yan;Wei-Hua Chieng
Affiliations:
-;-
Venue:
Computers & Mathematics with Applications
Year:
2006

Citing 7
Cited 0

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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.