Report
Computing the rank and a small nullspace basis of a polynomial matrix
| Τίτλος: | Computing the rank and a small nullspace basis of a polynomial matrix |
|---|---|
| Συγγραφείς: | Laboratoire de l'informatique du parallélisme, Storjohann, Arne, Villard, Gilles |
| Πηγή: | http://www.ens-lyon.fr/LIP/Pub/Rapports/RR/RR2005/RR2005-03.pdf. |
| Έτος έκδοσης: | 2005 |
| Συλλογή: | LARA - Libre accès aux rapports scientifiques et techniques (INIST - Institut de l'Information Scientifique et Technique / CNRS) |
| Θεματικοί όροι: | Linear algebra, polynomial matrix, matrix multiplication, nullspace basis, minimal polynomial basis, randomized algorithm |
| Περιγραφή: | (eng) We reduce the problem of computing the rank and a nullspace basis of a univariate polynomial matrix to polynomial matrix multiplication. For an input n x n matrix of degree d over a field K we give a rank and nullspace algorithm using about the same number of operations as for multiplying two matrices of dimension n and degree d. If the latter multiplication is done in MM(n,d)=softO((n^omega)d) operations, with omega the exponent of matrix multiplication over K, then the algorithm uses softO(MM(n,d)) operations in K. For m x n matrices of rank r and degree d, the cost expression is softO(nmr^(omega -2)d). The softO notation indicates some missing logarithmic factors. The method is randomized with Las Vegas certification. We achieve our results in part through a combination of matrix Hensel high-order lifting and matrix minimal fraction reconstruction, and through the computation of minimal or small degree vectors in the nullspace seen as a K[x]-module. |
| Τύπος εγγράφου: | report |
| Περιγραφή αρχείου: | 2+24p; 420284 bytes; 23 bytes; application/pdf; application/octet-stream |
| Γλώσσα: | English |
| Relation: | LIP-RR - 2005-03; http://hdl.handle.net/2332/512 |
| Διαθεσιμότητα: | http://hdl.handle.net/2332/512 |
| Αριθμός Καταχώρησης: | edsbas.3BA387B8 |
| Βάση Δεδομένων: | BASE |
καταχωρήστε σχόλιο πρώτοι!