Algorithms for Large Integer Matrix Problems

Authors:
Mark Giesbrecht;Michael J. Jacobson, Jr.;Arne Storjohann
Affiliations:
-;-;-
Venue:
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Year:
2001

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Abstract

New algorithms are described and analysed for solving various problems associated with a large integer matrix: computing the Hermite form, computing a kernel basis, and solving a system of linear diophantine equations. The algorithms are space-efficient and for certain types of input matrices -- for example, those arising during the computation of class groups and regulators--are faster than previous methods. Experiments with a prototype implementation support the running time analyses.