In this paper, a matrix form analoguous to the companion matrix which is often encountered in the theory of one dimensional (1-D) linear control systems is suggested for a class of polynomials in two indeterminates and real coefficients, here referred to as two dimensional (2-D) polynomials. These polynomials arise in the context of the theory of 2-D linear discrete control systems. Necessary a...

In this paper we will consider a partial reduction for nonhomogeneous linear systems of the operator equations with the system matrix in the companion form and with different operators. As a result of this method we will get an equivalent system consisting of the linear operator equations having only one or two variables. Homogeneous part of the equation in one unknown is obtained using general...

A stable algorithm to compute the roots of polynomials is presented. The roots are found by computing the eigenvalues of the associated companion matrix by Francis’s implicitly shifted QR algorithm. A companion matrix is an upper Hessenberg matrix that is unitary-plus-rankone, that is, it is the sum of a unitary matrix and a rank-one matrix. These properties are preserved by iterations of Franc...

Inspired by Rearick (1968), we introduce two new operators, LOG and EXP. The LOG operates on generalized Fibonacci polynomials giving generalized Lucas polynomials. The EXP is the inverse of LOG. In particular, LOG takes a convolution product of generalized Fibonacci polynomials to a sum of generalized Lucas polynomials and EXP takes the sum to the convolution product. We use this structure to ...

The PolyMAX estimator is used intensively in modal analysis applications nowadays. The main advantages are its speed and the very clear stabilization diagrams it yields. Recently, an algorithm allowing a fast calculation of confidence intervals has been derived for frequency-domain least-squares estimators based on a common-denominator model. In this contribution, the approach is extended to th...

In recent years, there has been a growing interest in companion matrices. Sparse matrices are well known: every sparse matrix is equivalent to Hessenberg of particular simple type. Recently, Deaett et al. [Electron. J. Linear Algebra, 35:223--247, 2019] started the systematic study nonsparse They proved that nonderogatory, although not necessarily matrix. this paper, which unit described. matri...

In 1990 Krivine (1990b) introduced the notion of storage operators. They are λ-terms which simulate call-by-value in the call-by-name strategy. Krivine (1990b) has shown that there is a very simple type in the AF2 type system for storage operators using Gődel translation from classical to intuitionistic logic. Parigot (1993a) and Krivine (1994) have shown that storage operators play an importan...

This note presents the explicit form of the Laplace transform of the state transition matrix in the case of a system matrix being a companion matrix. Starting from this special case, we show how to compute the Laplace transform of the state transition matrix for any system matrix.1