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Integer matrix diagonalization. (English) Zbl 0880.68066
Summary: We consider algorithms for computing the Smith normal form of integer matrices. A variety of different strategies have been proposed, primarily aimed at avoiding the major obstacle that occurs in such computations – explosive growth in size of intermediate entries. We present a new algorithm with excellent performance.
We investigate the complexity of such computations, indicating relationships with NP-complete problems. We also describe new heuristics which perform well in practice. We present experimental evidence which shows our algorithm outperforming previous methods.

MSC:
68W30 Symbolic computation and algebraic computation
65F30 Other matrix algorithms (MSC2010)
65Y20 Complexity and performance of numerical algorithms
15B36 Matrices of integers
15A21 Canonical forms, reductions, classification
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