Bini, D. A. and Gemignani, Luca (1997) *Fast fraction-free triangularization of Bezoutians with applications to sub-resultant chain computation.* Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT.

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## Abstract

An algorithm for the computation of the LU factorization over the integers of an $n\times n$ Bezoutian $B$ is presented. The algorithm requires $O(n^2)$ arithmetic operations and involves integers having at most $O(n\log nc)$ bits, where $c$ is an upper bound of the moduli of the integer entries of $B$. As an application, by using the correlations between Bezoutians and the Euclidean scheme, we devise a new division-free algorithm for the computation of the polynomial pseudo-remainder sequence of two polynomials of degree at most $n$ in $O(n^2)$ arithmetic operations. The growth of the length of the integers involved in the computation is kept at the minimum value, i.e., $O(n\log nc)$ bits, no matter if the sequence is normal or not, where $c$ is an upper bound of the moduli of the input coefficients. The algorithms, that rely on the Bareiss technique and on the properties of the Schur complements of Bezoutians , improve the previous ones.

Item Type: | Book |
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Uncontrolled Keywords: | |

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 11:13 |

Last Modified: | 23 Jan 2015 11:13 |

URI: | http://eprints.adm.unipi.it/id/eprint/1980 |

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