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EFFICIENT ALGORITHMS FOR THE DECOMPOSITION OF MATRIX ALGEBRAS

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Author
Eberly, Wayne
Accessioned
2008-02-26T20:31:26Z
Available
2008-02-26T20:31:26Z
Computerscience
1999-05-27
Issued
1990-08-01
Subject
Computer Science
Type
unknown
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Abstract
We consider the bit-complexity of the decomposition of semi-simple algebras over finite fields and number fields, and of simple algebras over C and R, for matrix algebras with bases consisting of matrices over a number field. Exact computations in number fields are performed symbolically. We present new probabilistic and deterministic polynomial-time algorithms for the decomposition of semi-simple algebras over the above concrete fields. The algorithms are somewhat simpler than the algorithm previously given by Friedl and Ronyai; the probabilistic algorithm suggests a modification that might improve the performance of the original algorithm in the average case. The new methods also provide parallel (NC) reductions from the decomposition of semi-simple algebras to the problem of factoring polynomials over fields, as well as efficient parallel algorithms for the decomposition of semi-simple algebras over (small) finite fields. We also extend the methods of Eberly [8] and Babai and Ronyai [1] for the decomposition of simple algebras over C, to obtain a new probabilistic polynomial-time algorithm for the decomposition of simple algebras over R. This is the first (Boolean) polynomial-time algorithm for this problem.
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We are currently acquiring citations for the work deposited into this collection. We recognize the distribution rights of this item may have been assigned to another entity, other than the author(s) of the work.If you can provide the citation for this work or you think you own the distribution rights to this work please contact the Institutional Repository Administrator at digitize@ucalgary.ca
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University of Calgary
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Science
Doi
http://dx.doi.org/10.11575/PRISM/30589
Uri
http://hdl.handle.net/1880/45471
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