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Recovering a perturbation of a matrix polynomial from a perturbation of its first companion linearization
Örebro University, School of Science and Technology.ORCID iD: 0000-0001-9110-6182
2022 (English)In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, no 62, p. 69-88Article in journal (Refereed) Published
Abstract [en]

A number of theoretical and computational problems for matrix polynomials are solved by passing to linearizations. Therefore a perturbation theory, that relates perturbations in the linearization to equivalent perturbations in the corresponding matrix polynomial, is needed. In this paper we develop an algorithm that finds which perturbation of matrix coefficients of a matrix polynomial corresponds to a given perturbation of the entire linearization pencil. Moreover we find transformation matrices that, via strict equivalence, transform a perturbation of the linearization to the linearization of a perturbed polynomial. For simplicity, we present the results for the first companion linearization but they can be generalized to a broader class of linearizations.

Place, publisher, year, edition, pages
Springer, 2022. no 62, p. 69-88
Keywords [en]
Matrix polynomial, Matrix pencil, Linearization, Perturbation theory
National Category
Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-91954DOI: 10.1007/s10543-021-00878-9ISI: 000652423700001Scopus ID: 2-s2.0-85106339264OAI: oai:DiVA.org:oru-91954DiVA, id: diva2:1557760
Note

Funding Agency:

Örebro University  

Available from: 2021-05-27 Created: 2021-05-27 Last updated: 2023-12-08Bibliographically approved

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Dmytryshyn, Andrii

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