Block solution of sparse linear systems over GF (q)
Gilles Villard · ACM SIGSAM Bulletin · 1998
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 .