Random Krylov Spaces over Finite Fields
- 1 January 2003
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Discrete Mathematics
- Vol. 16 (2) , 276-287
- https://doi.org/10.1137/s089548010139388x
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 increasesKeywords
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