Solving sparse linear equations over finite fields
IEEE Transactions on Information Theory
On rank properties of Toeplitz matrices over finite fields
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
On randomized Lanczos algorithms
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
On Wiedemann's Method of Solving Sparse Linear Systems
AAECC-9 Proceedings of the 9th International Symposium, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
Black box linear algebra with the linbox library
Black box linear algebra with the linbox library
Efficient matrix rank computation with application to the study of strongly regular graphs
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
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This paper develops preconditioners for singular black box matrix problems. We introduce networks of arbitrary radix switches for matrices of any square dimension, and we show random full Toeplitz matrices are adequate switches for these networks. We also show a random full Toeplitz matrix to satisfy all requirements of the Kaltofen-Saunders black box matrix rank algorithm without requiring a diagonal multiplier.