Abstract
Motivated by a connection with block iterative methods for solving linear systems over finite fields, we consider the probability that the Krylov space generated by a fixed linear mapping and a random set of elements in a vector space over a finite field equals the space itself. We obtain an exact formula for this probability and from it we derive good lower bounds that approach 1 exponentially fast as the size of the set increases.
Original language | English |
---|---|
Pages (from-to) | 276-287 |
Number of pages | 12 |
Journal | SIAM Journal on Discrete Mathematics |
Volume | 16 |
Issue number | 2 |
DOIs | |
Publication status | Published - Feb 2003 |
Externally published | Yes |