Polynomial root radius optimization with affine constraints / Julie Eaton, Sara Grundel, Mert Gürbüzbalaban, Michael L. Overton
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Discovery
870663704
URN
urn:nbn:de:gbv:3:2-64656
DOI
ISBN
ISSN
Beiträger
Erschienen
Magdeburg : Max Planck Institute for Dynamics of Complex Technical Systems, March 3, 2015
Umfang
1 Online-Ressource (14 Seiten = 0,4 MB) : Diagramme
Ausgabevermerk
Sprache
eng
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Inhaltliche Zusammenfassung
Abstract: The root radius of a polynomial is the maximum of the moduli of its roots (zeros). We consider the following optimization problem: minimize the root radius over monic polynomials of degree n, with either real or complex coefficients, subject to k consistent affine constraints on the coefficients. We show that there always exists an optimal polynomial with at most k − 1 inactive roots, that is, whose modulus is strictly less than the optimal root radius. We illustrate our results using some examples arising in feedback control.
Schriftenreihe
Max Planck Institute Magdeburg Preprints ; 14-24 ppn:870173030