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Geometry of Matrix Polynomial Spaces
Umeå University, Faculty of Science and Technology, Department of Computing Science. School of Science and Technology, Örebro University, Örebro, Sweden. (UMIT)
Umeå University, Faculty of Science and Technology, Department of Computing Science. (UMIT)
Umeå University, Faculty of Science and Technology, Department of Computing Science. (UMIT)
Department of Mathematical Engineering, Université catholique de Louvain, Louvain-la-Neuve, Belgium.
2020 (English)In: Foundations of Computational Mathematics, ISSN 1615-3375, E-ISSN 1615-3383, Vol. 20, no 3, p. 423-450Article in journal (Refereed) Published
Abstract [en]

We study how small perturbations of general matrix polynomials may change their elementary divisors and minimal indices by constructing the closure hierarchy (stratification) graphs of matrix polynomials' orbits and bundles. To solve this problem, we construct the stratification graphs for the first companion Fiedler linearization of matrix polynomials. Recall that the first companion Fiedler linearization as well as all the Fiedler linearizations is matrix pencils with particular block structures. Moreover, we show that the stratification graphs do not depend on the choice of Fiedler linearization which means that all the spaces of the matrix polynomial Fiedler linearizations have the same geometry (topology). This geometry coincides with the geometry of the space of matrix polynomials. The novel results are illustrated by examples using the software tool StratiGraph extended with associated new functionality.

Place, publisher, year, edition, pages
Springer, 2020. Vol. 20, no 3, p. 423-450
Keywords [en]
Matrix polynomials, Stratifications, Matrix pencils, Fiedler linearization, Canonical structure information, Orbit, Bundle
National Category
Computational Mathematics Computer and Information Sciences
Identifiers
URN: urn:nbn:se:umu:diva-163512DOI: 10.1007/s10208-019-09423-1ISI: 000531825900002Scopus ID: 2-s2.0-85068193369OAI: oai:DiVA.org:umu-163512DiVA, id: diva2:1353896
Funder
eSSENCE - An eScience CollaborationSwedish Research Council, E0485301Available from: 2019-09-24 Created: 2019-09-24 Last updated: 2020-10-15Bibliographically approved

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Dmytryshyn, AndriiJohansson, StefanKågström, Bo

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Citation style
  • apa
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