Total nonnegativity of finite Hurwitz matrices and root location of polynomials

Publikationstyp: Working Paper/Technical Report
Publikationsstatus: Published
URI (zitierfähiger Link): http://nbn-resolving.de/urn:nbn:de:bsz:352-2--t62blplni8h73
Autor/innen: Adm, Mohammad; Garloff, Jürgen; Tyaglov, Mikhail
Erscheinungsjahr: 2017
Schriftenreihe: Konstanzer Schriften in Mathematik ; 368
Zusammenfassung:
In 1970, B.A. Asner, Jr., proved that for a real quasi-stable polynomial, i.e., a polynomial whose zeros lie in the closed left half-plane of the complex plane, its finite Hurwitz matrix is totally nonnegative, i.e., all its minors are nonnegative, and that the converse statement is not true. In this work, we explain this phenomenon in detail, and provide necessary and sufficient conditions for a real polynomial to have a totally nonnegative finite Hurwitz matrix.
MSC-Klassifikation: 15B48, 26C10, 15A18, 15B05
Fachgebiet (DDC): 510 Mathematik
Schlagwörter: Hurwitz matrix, totally nonnegative matrix, stable polynomial, quasi-stable polynomial, R-function
Link zur Lizenz: Nutzungsbedingungen
Universitätsbibliographie: Ja

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ADM, Mohammad, Jürgen GARLOFF, Mikhail TYAGLOV, 2017. Total nonnegativity of finite Hurwitz matrices and root location of polynomials

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