Symmetric Subresultants and Applications
| dc.creator | Brunie, Cyril | |
| dc.creator | Picart, Philippe Saux | |
| dc.date | 2006-12-22 | |
| dc.date | 2007-03-29 | |
| dc.date.accessioned | 2026-07-07T07:54:48Z | |
| dc.date.available | 2026-07-07T07:54:48Z | |
| dc.description | Schur's transforms of a polynomial are used to count its roots in the unit disk. These are generalized them by introducing the sequence of symmetric sub-resultants of two polynomials. Although they do have a determinantal definition, we show that they satisfy a structure theorem which allows us to compute them with a type of Euclidean division. As a consequence, a fast algorithm based on a dichotomic process and FFT is designed. We prove also that these symmetric sub-resultants have a deep link with Toeplitz matrices. Finally, we propose a new algorithm of inversion for such matrices. It has the same cost as those already known, however it is fraction-free and consequently well adapted to computer algebra. | |
| dc.identifier | https://arxiv.org/abs/cs/0612119 | |
| dc.identifier | http://arxiv.org/abs/cs/0612119 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/126751 | |
| dc.subject | Symbolic Computation | |
| dc.title | Symmetric Subresultants and Applications | |
| dc.type | text |