Total nonnegativity of finite Hurwitz matrices and root location of polynomials
| Type of Publication: | Working Paper/Technical Report |
| Publication status: | Published |
| URI (citable link): | http://nbn-resolving.de/urn:nbn:de:bsz:352-2--t62blplni8h73 |
| Author: | Adm, Mohammad; Garloff, Jürgen; Tyaglov, Mikhail |
| Year of publication: | 2017 |
| Series: | Konstanzer Schriften in Mathematik ; 368 |
| Summary: |
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 Classification: | 15B48, 26C10, 15A18, 15B05 |
| Subject (DDC): | 510 Mathematics |
| Keywords: | Hurwitz matrix, totally nonnegative matrix, stable polynomial, quasi-stable polynomial, R-function |
| Link to License: | In Copyright |
| Bibliography of Konstanz: | Yes |
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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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