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

作者：Wilkening Jon^*; Yu Jia

来源：Journal of Symbolic Computation, 2011, 46(1): 1-22.

DOI：10.1016/j.jsc.2010.06.025

• Matrix polynomial
• Canonical forms
• Smith form
• Jordan chain
• Symbolic computation

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.

• 出版日期2011-1