TY - JOUR
A1 - Adm, Mohammad
A1 - Garloff, Jürgen
A1 - Tyaglov, Mikhail
T1 - Total nonnegativity of finite Hurwitz matrices and root location of polynomials
JF - Journal of Mathematical Analysis and Applications
N2 - 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.
KW - Hurwitz matrix
KW - Totally nonnegative matrix
KW - Stable polynomial
KW - Quasi-stable polynomial
KW - R-function
Y1 - 2018
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bsz:kon4-opus4-14614
SN - 0022-247X
SN - 1096-0813
VL - 467
IS - 1
SP - 148
EP - 170
PB - Elsevier
ER -
TY - CHAP
A1 - Adm, Mohammad
A1 - Garloff, Jürgen
A1 - Tyaglov, Mikhail
T1 - Root location of polynomials whose finite Hurwitz matrix is totally nonnegative
T2 - Sixth Palestinian Conference on Modern Trends in Mathematics and Physics (PCMTMP-VI), 5. - 8. August 2018, Palestine Technical University Kadoorei, Palästina
KW - Totally nonnegative matrix
KW - Hurwitz matrix
KW - Stable polynomial
KW - Quasi-stable polynomial
Y1 - 2018
ER -