Random Krylov Spaces over Finite Fields

Authors:
Richard P. Brent;Shuhong Gao;Alan G. B. Lauder
Affiliations:
-;-;-
Venue:
SIAM Journal on Discrete Mathematics
Year:
2003

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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.