The notion of Bezout matrix is an essential tool in studying broad variety of subjects: zeroes of polynomials, stability of differential equations, rational transformations of algebraic curves, systems of commuting nonselfadjoint operators, boundaries of quadrature domains etc. We present a survey of several properties of Bezout matrices and their applications in all mentioned topics. We use th...

This paper presents a generalized Bezout theorem which can be used to determine a tighter lower bound of the number of distinct points of intersection of two or more plane curves. A new approach to determine a lower bound on the minimum distance for algebraic-geometric codes defined from a class of plane curves is introduced, based on the generalized Bezout theorem. Examples of more efficient l...

This paper examines the optimum design of FIR precoders or equalizers for multiple-input multiple-output (MIMO) frequencyselective wireless channels. For the case of a left-coprime FIR channel, which arises generically when the number nT of transmit antennas is larger than the number nR of receive antennas, the Bezout matrix identity can be employed to design an FIR MIMO precoder that equalizes...

Given two polynomials with coeecients over Zk], the associated Bezout matrix B(k) with entries over Zk] deenes a parametric family of Bezout matrices with entries over Z. It is intended in this paper to propose a hybrid approach for determining the inertia of B(k) for any value of k in some real interval. This yields an eecient solution to certain root-location problems for bivariate polynomial...

In a general algebraic framework, starting with a bicoprime factorization P = N,,DINpl, we obtain a right-coprime factorization N D -*, a left-coprime factorization D;’mPp, and the generalized Bezout idPen&ies associated with the pairs ( N p , 0,) and ( D p , mp). We express the set of all H-stabilizing compensators for P in the unity-feedback configuration S ( P , C) in terms of (N,,, D , N,,)...

In this paper we derive some properties of the Bezout matrix and relate the Fisher information matrix for a stationary ARMA process to the Bezoutian. Some properties are explained via realizations in state space form of the derivatives of the white noise process with respect to the parameters. A factorization of the Fisher information matrix as a product in factors which involve the Bezout matr...

A piecewise algebraic curve is a curve defined by the zero set of a bivariate spline function. Given two bivariate spline spaces Sm Δ and S t n Δ over a domain D with a partition Δ, the Bezout number BN m,r;n,t;Δ is defined as the maximum finite number of the common intersection points of two arbitrary piecewise algebraic curves f x, y 0 and g x, y 0, where f x, y ∈ Sm Δ and g x, y ∈ Sn Δ . In ...