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.
Original language | English |
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Pages (from-to) | 605-620 |
Number of pages | 16 |
Journal | Computers and Mathematics with Applications |
Volume | 51 |
Issue number | 3-4 |
DOIs | |
State | Published - 1 Feb 2006 |
Keywords
- Approximate divisibility
- Approximate GCD
- Multiple root
- Root finding
- Zero finding, Polynomial GCD