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New structure theorems for subresultants
Abstract : We give a new structure theorem for subresultants precising their gap structure and derive from it a new algorithm for computing them. If $d$ is a bound on the degrees and $\tau$ a bound on the bitsize of the minors extracted from Sylvester matrix, our algorithm has $O(d^2)$ arithmetic operations and size of intermediate computations $2\tau$. The key idea is to precise the relations between the successive Sylvester matrix of $A$ and $B$ in one hand and of $A$ and $XB$ on the other hand, using the notion of G-remainder we introduce. We also compare our new algorithm with another algorithm with the same characteristics given by L. Ducos.
https://hal.inria.fr/inria-00099274
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Submitted on : Tuesday, September 26, 2006 - 8:52:18 AM
Last modification on : Friday, February 4, 2022 - 4:17:49 AM
Contributor : Publications Loria Connect in order to contact the contributor
Submitted on : Tuesday, September 26, 2006 - 8:52:18 AM
Last modification on : Friday, February 4, 2022 - 4:17:49 AM
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