Abstract
Popov forms and weak Popov forms of matrices over noncommutative valuation domains are defined and discussed. Two new algorithms to construct these Popov forms are given, along with a description of some of their applications.
Chapter PDF
Similar content being viewed by others
References
Abramov, S., Bronstein, M.: Linear Algebra for skew-polynomial matrices. INRIA (preprint)
Artin, E.: Geometric Algebra. Interscience Publishers, Inc., Hoboken (1957)
Beckermann, B., Cheng, H., Labahn, G.: Fraction-free row reduction of matrices of Ore polynomials. In: Proceedings of ISSAC 2002, pp. 8–15. ACM Press, New York (2002)
Beckermann, B., Labahn, G., Villard, G.: Shifted Normal Forms of Polynomial Matrices. In: Proceedings of ISSAC 1999, pp. 189–196. ACM Press, New York (1999)
Cohn, P.M.: Skew Fields. Cambridge University Press, Cambridge (1995)
Giesbrecht, M., Labahn, G., Zhang, Y.: Popov forms for multivariate polynomial matrices (preprint)
Jacobson, N.: The Theory of Rings. American Math. Soc., New York (1943)
Kailath, T.: Linear Systems. Prentice-Hall, Englewood Cliffs (1980)
Mulders, T., Storjohann, A.: On lattice reduction for polynomial matrices. Journal of Symbolic Computation 35, 377–401 (2003)
Ore, O.: Theory of non-commutative polynomials. Annals of Mathematics 34(22), 480–508 (1933)
Popov, V.: Invariant description of linear, time-invariant controllable systems. SIAM J. Control. 10(2), 252–264 (1972)
Schilling, O.: The Theory of Valuations. Math. Surveys No. IV. Amer. Math. Soc., New York (1950)
Villard, G.: Computing Popov and Hermite forms of polynomial matrices. In: Proceeding of ISSAC 1996, pp. 250–258. ACM Press, New York (1996)
von zur Gathen, J.: Hensel and Newton methods in valuation rings. Mathematics of Computation 42, 637–661 (1984)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Giesbrecht, M., Labahn, G., Zhang, Y. (2005). Computing Valuation Popov Forms. In: Sunderam, V.S., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds) Computational Science – ICCS 2005. ICCS 2005. Lecture Notes in Computer Science, vol 3516. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11428862_84
Download citation
DOI: https://doi.org/10.1007/11428862_84
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26044-8
Online ISBN: 978-3-540-32118-7
eBook Packages: Computer ScienceComputer Science (R0)Springer Nature Proceedings Computer Science