Fraction-free row reduction of matrices of skew polynomials

Authors:
Bernhard Beckermann;Howard Cheng;George Labahn
Affiliations:
Université des Sciences et Technologies de Lille, France;University of Waterloo, Waterloo, Canada;University of Waterloo, Waterloo, Canada
Venue:
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Year:
2002

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Abstract

We present a new algorithm for row reduction of a matrix of skew polynomials. The algorithm can be used for finding full rank decompositions and other rank revealing transformations of matrices of skew polynomials. The algorithm is intended for computation in exact arithmetic domains where the growth of coefficients in intermediate computations is a central concern. This coefficient growth is controlled by using fraction-free methods. This allows us to obtain a polynomial-time algorithm: for an m x s matrix of input skew polynomials of degree N with coefficients whose lengths are bounded by K the algorithm has a worst case complexity of O(m5s4N4K2) bit operations.