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TitleNormal forms for general polynomial matrices
Author(s) Bernhard Beckermann, George Labahn, Gilles Villard
TypeArticle in Journal
AbstractWe 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 fraction-free 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.
KeywordsPopov normal form, Hermite normal form, Matrix Gcd, Exact arithmetic, Fraction-free algorithm
URL http://www.sciencedirect.com/science/article/pii/S0747717106000022
JournalJournal of Symbolic Computation
Pages708 - 737
Translation No
Refereed No