Annular bounds for the zeros of a polynomial from companion matrices

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

scholarly journals Toeplitz nonnegative realization of spectra via companion matrices

2019 ◽  
Vol 7 (1) ◽  
pp. 230-245
Author(s):  
Macarena Collao ◽  
Mario Salas ◽  
Ricardo L. Soto
Keyword(s):  
Eigenvalue Problem ◽  
Half Plane ◽  
Toeplitz Matrix ◽  
Toeplitz Matrices ◽  
Nonnegative Matrix ◽  
Inverse Eigenvalue Problem ◽  
Complex Numbers ◽  
Inverse Eigenvalue ◽  
Companion Matrices ◽  
Solution Matrix

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.

scholarly journals Bounds on polynomial roots using intercyclic companion matrices

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

scholarly journals Three-way companion matrices of three-variable polynomials

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

A noncommutative spectral theorem for operator entried companion matrices

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

scholarly journals Explicit polar decomposition of companion matrices

1996 ◽  
Vol 1 ◽  
Author(s):  
Pauline Van den Driessche ◽  
Harald Wimmer
Keyword(s):  
Polar Decomposition ◽  
Companion Matrices

scholarly journals On the stabilizer of companion matrices

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

scholarly journals Linear fractional transforms of companion matrices

1979 ◽  
Vol 20 (2) ◽  
pp. 129-132 ◽  
Author(s):  
N. J. Young
Keyword(s):  
Characteristic Polynomial ◽  
Canonical Form ◽  
Stability Theory ◽  
Companion Matrix ◽  
Arbitrary Field ◽  
Companion Matrices ◽  
Image Position ◽  
Fractional Transforms

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.

scholarly journals Backward stability of polynomial root-finding using Fiedler companion matrices

2015 ◽  
pp. dru057 ◽  
Author(s):  
Fernando de Terán ◽  
Froilán M. Dopico ◽  
Javier Pérez
Keyword(s):  
Root Finding ◽  
Backward Stability ◽  
Companion Matrices ◽  
Polynomial Root Finding

scholarly journals An algorithm for computing the eigenvalues of block companion matrices

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