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