Method for finding multiple roots of polynomials

Chang Dau Yan, Wei-Hua Chieng*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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 languageEnglish
Pages (from-to)605-620
Number of pages16
JournalComputers and Mathematics with Applications
Issue number3-4
StatePublished - 1 Feb 2006


  • Approximate divisibility
  • Approximate GCD
  • Multiple root
  • Root finding
  • Zero finding, Polynomial GCD

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