Annular bounds for the zeros of a polynomial from companion matrices

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Pintu Bhunia ◽  
Kallol Paul
Keyword(s):  

2019 ◽  
Vol 7 (1) ◽  
pp. 230-245
Author(s):  
Macarena Collao ◽  
Mario Salas ◽  
Ricardo L. Soto

Abstract The nonnegative inverse eigenvalue problem (NIEP) is the problem of finding conditions for the existence of an n × n entrywise nonnegative matrix A with prescribed spectrum Λ = {λ1, . . ., λn}. If the problem has a solution, we say that Λ is realizable and that A is a realizing matrix. In this paper we consider the NIEP for a Toeplitz realizing matrix A, and as far as we know, this is the first work which addresses the Toeplitz nonnegative realization of spectra. We show that nonnegative companion matrices are similar to nonnegative Toeplitz ones. We note that, as a consequence, a realizable list Λ= {λ1, . . ., λn} of complex numbers in the left-half plane, that is, with Re λi≤ 0, i = 2, . . ., n, is in particular realizable by a Toeplitz matrix. Moreover, we show how to construct symmetric nonnegative block Toeplitz matrices with prescribed spectrum and we explore the universal realizability of lists, which are realizable by this kind of matrices. We also propose a Matlab Toeplitz routine to compute a Toeplitz solution matrix.



2018 ◽  
Vol 539 ◽  
pp. 94-116
Author(s):  
Kevin N. Vander Meulen ◽  
Trevor Vanderwoerd


1981 ◽  
Vol 37 ◽  
pp. 55-75 ◽  
Author(s):  
Krzysztof Gałlkowski
Keyword(s):  


1981 ◽  
Vol 10 (1) ◽  
pp. 45-51
Author(s):  
John de Pillis ◽  
Michael Neumann


Author(s):  
Pauline Van den Driessche ◽  
Harald Wimmer


1993 ◽  
Vol 69 (5) ◽  
pp. 140-143 ◽  
Author(s):  
Javier Gomez-Calderon
Keyword(s):  


1979 ◽  
Vol 20 (2) ◽  
pp. 129-132 ◽  
Author(s):  
N. J. Young

Questions about polynomials can be turned into questions about matrices by associating with the polynomial(over an arbitrary field) its companion matrixwhich has p/an as its characteristic polynomial. This technique is often used in stability theory, as indicated in [1]; companion matrices also occur in the theory of the rational canonical form.



2015 ◽  
pp. dru057 ◽  
Author(s):  
Fernando de Terán ◽  
Froilán M. Dopico ◽  
Javier Pérez


2012 ◽  
Vol 62 (2) ◽  
pp. 261-287 ◽  
Author(s):  
Katrijn Frederix ◽  
Steven Delvaux ◽  
Marc Van Barel
Keyword(s):  


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