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A block algorithm of Lanczos type for solving sparse systems of linear equations
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M. A. Cherepnev
Published/Copyright:
May 9, 2008
Abstract
We suggest a new block algorithm for solving sparse systems of linear equations over GF(2) of the form
where A is a symmetric matrix, F = GF(2) is a field with two elements. The algorithm is constructed with the use of matrix Padé approximations. The running time of the algorithm with the use of parallel calculations is max{O(dN2/n), O(N2)}, where d is the maximal number of nonzero elements over all rows of the matrix A. If d < Cn for some absolute constant C, then this estimate is better than the estimate of the running time of the well-known Montgomery algorithm.
Received: 2007-04-18
Published Online: 2008-05-09
Published in Print: 2008-March
© de Gruyter 2008
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Articles in the same Issue
- Random polynomials over a finite field
- Random permutations with cycle lengths in a given finite set
- The Kloss convergence principle for products of random variables with values in a compact group and distributions determined by a Markov chain
- On enumeration of labelled connected graphs by the number of cutpoints
- Skew Laurent series rings and the maximum condition on right annihilators
- A block algorithm of Lanczos type for solving sparse systems of linear equations
- On complexity of the anti-unification problem
- Classification of indecomposable Abelian (v, 5)-groups
