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Asymptotically fast polynomial matrix algorithms for multivariable systems (2005)

Abstract
We present the asymptotically fastest known algorithms for some basic problems on univariate polynomial matrices: rank, nullspace, determinant, generic inverse, reduced form. We show that they essentially can be reduced to two computer algebra techniques, minimal basis computations and matrix fraction expansion/reconstruction, and to polynomial matrix multiplication. Such reductions eventually imply that all these problems can be solved in about the same amount of time as polynomial matrix multiplication.

Publication details
Download http://hal.ccsd.cnrs.fr/ccsd-00008211/en/
Source http://hal.ccsd.cnrs.fr/docs/00/03/53/68/PDF/approx.pdf
Publisher HAL - CCSd - CNRS
Contributors Gilles Villard
Repository CCSd/HAL : e-articles server (based on gBUS) (France)
Keywords Cognitive science/Computer science, Computer Science/Symbolic Computation, Computer Science/Computational Complexity
Language Englisch
Coverage linear algebra:polynomial matrix:matrix rank:matrix determinant:nullspace basis:matrix inversion:matrix reduced form

Cited publications (2)
Computing the Rank and a Small Nullspace Basis of a Polynomial Matrix (2005)
Minimal Degree Coprime Factorization of Rational Matrices (1999)