For a generic n-degree polynomial system which contains n+1 polynomials in n variables, we give the construction of the generic mixed Cayley-Sylvester resultant matrix. There are n− 1 generic mixed Cayley-Sylvester resultant matrices between the classical Cayley resultant matrix and the classical Sylvester resultant matrix. The entries of these new resultant matrix are of degree m(1 < m < n + 1...

This paper is concerned with the study of an arbitrary polynomial optimization via a convex relaxation, namely a semidefinite program (SDP). The existence of a rank-1 matrix solution for the SDP relaxation guarantees the recovery of a global solution of the original problem. The main objective of this work is to show that an arbitrary polynomial optimization has an equivalent formulation in the...

The easiest matrices to compute with are the diagonal ones. The sum and product of diagonal matrices can be computed componentwise along the main diagonal, and taking powers of a diagonal matrix is simple too. All the complications of matrix operations are gone when working only with diagonal matrices. If a matrix A is not diagonal but can be conjugated to a diagonal matrix, say D := PAP−1 is d...

We show that the computation of the Popov form of Ore polynomial matrices can be formulated as a problem of computing the left nullspace of such matrices. While this technique is already known for polynomial matrices, the extension to Ore polynomial matrices is not immediate because multiplication of the matrix entries is not commutative. A number of results for polynomial matrices are extended...

Linear Complementarity Problems (LCPs) belong to the class of NP-complete problems. Therefore we can not expect a polynomial time solution method for LCPs without requiring some special property of the coefficient matrix. Following our recently published ideas we generalize affine scaling and predictor-corrector interior point algorithms to solve LCPs with general matrices in EP-sense, namely, ...

An extended innnite companion matrix ~ C 1 (D) and an innnite companion matrix C 1 (D) for a (nonmonic in general) matrix polynomial D is introduced and the nite companion matrix C(D) is generalized to the nonmonic case. These matrices generalize all properties of the innnite and nite companion (Frobenius) matrix corresponding to a scalar polynomial. In particular, C 1 (D) is a controllability ...

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...

Recently, there has been renewed interest in methods and techniques of reducing the confusion and uncertainty associated with the morass of spurious, computational poles that result from the traditional over-determined equation set in modal parameter estimation processes. In this paper, sev eral additional mechanisms for providing a clear stabilization, or consistency, diagram are presented. Am...

We study a variant of the univariate approximate GCD problem, where the coefficients of one polynomial f(x)are known exactly, whereas the coefficients of the second polynomial g(x)may be perturbed. Our approach relies on the properties of the matrix which describes the operator of multiplication by gin the quotient ring C[x]/(f). In particular, the structure of the null space of the multiplicat...

In this paper, a constructive general matrix factorization scheme is developed for extracting a nontrivial factor from a given nD (n > 2) polynomial matrix whose maximal order minors satisfy certain conditions. It is shown that three classes of nD polynomial matrices admit this kind of general matrix factorization. It turns out that minor prime factorization and determinantal factorization are ...