Details:
Title  Normal forms for general polynomial matrices  Author(s)  Bernhard Beckermann, George Labahn, Gilles Villard  Type  Article in Journal  Abstract  We present an algorithm for the computation of a shifted Popov normal form of a rectangular polynomial matrix. For specific input shifts, we obtain methods for computing the matrix greatest common divisor of two matrix polynomials (in normal form) and procedures for such polynomial normal form computations as those of the classical Popov form and the Hermite normal form. The method involves embedding the problem of computing shifted forms into one of computing matrix rational approximants. This has the advantage of allowing for fractionfree computations over integral domains such as Z [ z ] and K [ a 1 , … , a n ] [ z ] . In the case of rectangular matrix input, the corresponding multipliers for the shifted forms are not unique. We use the concept of minimal matrix approximants to introduce a notion of minimal multipliers and show how such multipliers are computed by our methods.  Keywords  Popov normal form, Hermite normal form, Matrix Gcd, Exact arithmetic, Fractionfree algorithm  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717106000022 
Language  English  Journal  Journal of Symbolic Computation  Volume  41  Number  6  Pages  708  737  Year  2006  Edition  0  Translation 
No  Refereed 
No 
