Abstract
Probabilistic algorithms based on the Krylov / Wiedemann or the Lanczos method to solve non homogeneous N x N systems Ax = b over a Galois field GF( q ), usually require 2 N matrix---vector products and O ( n 2+ o (1) ) additional arithmetic operations. Only the block Wiedemann algorithm, as given by Kaltofen in [6], has the least number (1+ε) N + O (1) of matrix---vector products of any known algorithm. We extend its analysis to the case of singular matrices A .
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