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GCD of polynomials and Bezout matrices

Gemignani, Luca (1997) GCD of polynomials and Bezout matrices. Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT.

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    A new algorithm is presented for computing an integer polynomial similar to the GCD of two polynomials $u(x)$ and $v(x)$ $\in {\bf Z}[x]$, $\deg(u(x))=n\geq \deg(v(x)) $. Our approach uses structured matrix computations involving Bezout matrices rather than Hankel matrices. In this way we reduce the computational costs showing that the new algorithm requires $O(n^2)$ arithmetical operations or $O(n^4(\log^2 n +l^2))$ Boolean operations, where $l=\max \{ \log(\parallel u(x) \parallel_{\infty}), \log(\parallel v(x) \parallel_{\infty})\}$.

    Item Type: Book
    Uncontrolled Keywords: gcd pf polynomials, Euclid's algorithm, Bezout matrices
    Subjects: Area01 - Scienze matematiche e informatiche > INF/01 - Informatica
    Divisions: Dipartimenti (until 2012) > DIPARTIMENTO DI INFORMATICA
    Depositing User: dott.ssa Sandra Faita
    Date Deposited: 23 Jan 2015 11:11
    Last Modified: 23 Jan 2015 11:11
    URI: http://eprints.adm.unipi.it/id/eprint/1967

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