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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