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The paper presents a new numerical method for the computation of the greatest common divisor (GCD) of an m-set of polynomials of R[s], P m,d, of maximal degree d. It is based on a previously proposed theoretical procedure (Karcanias, 1989) that characterizes the GCD of Pm,d as the output decoupling zero polynomial of a linear system S(Aˆ,Cˆ) that may be associated with Pm,d . The computation of the GCD is thus reduced to finding the finite zeros of the pencil sW-AW, where W is the unobservable subspace of S(Aˆ,Cˆ). If k=dim W, the GCD is determined as any nonzero entry of the kth compound Ck(sW-AˆW). The method defines the exact degree of GCD, works satisfactorily with any number of polynomials and evaluates successfully approximate solutions
Published in:
Automatic Control, IEEE Transactions on
(Volume:39
,
Issue:
5
)
Date of Publication: May 1994
- Page(s):
- 977 - 981
- ISSN :
- 0018-9286
- INSPEC Accession Number:
- 4702848
- Digital Object Identifier :
- 10.1109/9.284874
- Product Type:
- Journals & Magazines
- Date of Current Version :
- 06 August 2002
- Issue Date :
- May 1994
- Sponsored by :
- IEEE Control Systems Society
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