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Abstract: We analyse a randomized block algorithm proposed by Coppersmith for solving large sparse systems of linear equations, Aw = 0, over a finite field K =GF(q). It is a modification of an algorithm of Wiedemann. Coppersmith has given heuristic arguments to understand why the algorithm works. But it was an open question to prove that it may produce a solution, with positive probability, for small finite fields e.g. for K =GF(2). We answer this question nearly completely. The algorithm uses two random ... (Update)
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...grouped and the number of iterations is reduced. There are two main advantages. The probabilities of success are improved in small nite elds [31]. Also, there is more parallelism (whith exactly the same number of matric vector products) However, the overall number of eld...
...for the computation undertaken here. The block Wiedemann algorithm performs well both theoretically and in practice. See [24, 25, 39, 40, 41] for several insights on the algorithm. The block Wiedemann algorithm is interesting in the fact that at least for one part of the...
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BibTeX entry: (Update)
Villard, G. (1997b). A study of Coppersmith's block Wiedemann algorithm using matrix polynomials. http://citeseer.ist.psu.edu/555962.html More
@misc{ vil97-1,
author = "Villard, G.",
title = "{A study of Coppersmith's block Wiedemann algorithm
using matrix polynomials}",
month = "Feb.",
note = "RR 975-I-M IMAG Grenoble, France",
year = "1997",
url = "citeseer.ist.psu.edu/555962.html" }
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