stable polynomial
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2020 ◽  
Vol 12 (5) ◽  
pp. 43
Author(s):  
Matthew Kim ◽  
Kelly Shin ◽  
Clara Lim ◽  
Selcuk Koyuncu

In this paper we provide some results that replace the condition ”real-zero” by the properties so-called x-substitution and y-substitution. We show that using these properties, we can still write the determinantal representation of a stable polynomial in terms of identity and Hermitian matrices.



2020 ◽  
Vol 36 (36) ◽  
pp. 210-213
Author(s):  
Stanisław Białas ◽  
Michał Góra

A Hurwitz stable polynomial of degree $n\geq1$ has a Hadamard factorization if it is a Hadamard product (i.e., element-wise multiplication) of two Hurwitz stable polynomials of degree $n$. It is known that Hurwitz stable polynomials of degrees less than four have a Hadamard factorization. It is shown that, for arbitrary $n\geq4$, there exists a Hurwitz stable polynomial of degree $n$ which does not have a Hadamard factorization.



2020 ◽  
Vol 58 (3) ◽  
pp. 1867-1892
Author(s):  
Mark Ainsworth ◽  
Charles Parker
Keyword(s):  


2018 ◽  
Vol 20 (6) ◽  
pp. 1375-1437 ◽  
Author(s):  
Diego Armentano ◽  
Carlos Beltrán ◽  
Peter Bürgisser ◽  
Felipe Cucker ◽  
Michael Shub


2016 ◽  
Vol 23 (2) ◽  
pp. 869-889 ◽  
Author(s):  
J. A. López-Renteria ◽  
B. Aguirre-Hernández ◽  
F. Verduzco


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