A local construction of the Smith normal form of a matrix polynomial

Details A local construction of the Smith normal form of a matrix polynomial A local construction of the Smith normal form of a matrix polynomial

2008-09-17

arxiv.org/abs/0809.2978v2

Computer Science

Symbolic Computation

26 pages, 6 figures; introduction expanded, 10 references added, two additional tests performed

Scientific paper

We present an algorithm for computing a Smith form with multipliers of a regular matrix polynomial over a field. This algorithm differs from previous ones in that it computes a local Smith form for each irreducible factor in the determinant separately and then combines them into a global Smith form, whereas other algorithms apply a sequence of unimodular row and column operations to the original matrix. The performance of the algorithm in exact arithmetic is reported for several test cases.

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