Recently, analytical methods for finding moments of random Vandermonde matrices with entries on the unit circle have been proposed in the literature. Vandermonde matrices play an important role in signal processing and wireless applications, among which the multiple-antenna channel modeling, precoding or sparse sampling theory. Recent investigations allowed to extend the combinatorial approach ...

The accurate solution of some of the main problems in numerical linear algebra (linear system solving, eigenvalue computation, singular value computation and the least squares problem) for a totally positive Bernstein-Vandermonde matrix is considered. Bernstein-Vandermonde matrices are a generalization of Vandermonde matrices arising when considering for the space of the algebraic polynomials o...

Several identification and control problems present nonlinearities that cannot be neglected and are often approximated by polynomials. In some previous works optimal set of interpolation nodes that minimizes the uncertainties of the approximation have been derived for the Vandermonde base that, however, can lead to ill-conditioned numerical problems. In this paper the conditions under which pol...

In this paper we study Stein equations where the coefficient matrices are in companion form. Solutions to such equations are relatively easy to compute as soon as one knows how to invert a Vandermonde matrix (in the generic case where all eigenvalues have multiplicity one) or a confluent Vandermonde matrix (in the general case). As an application we present a way to compute the Fisher informati...

An n-variate Vandermonde polynomial is the determinant of the n × n matrix where the ith column is the vector (1, xi, x 2 i , . . . , x n−1 i ) T . Vandermonde polynomials play a crucial role in the theory of alternating polynomials and occur in Lagrangian polynomial interpolation as well as in the theory of error correcting codes. In this work we study structural and computational aspects of l...

We show that an arbitrary Hankel matrix of a nite rank admits a Vandermonde decomposition: H = V T DV , where V is a con-uent Vandermonde matrix and D is a block diagonal matrix. This result was rst derived by Vandevoorde; our contribution here is a presentation that uses only linear algebra, speciically, the Jordan canonical form. We discuss the choices for computing this decomposition in only...

Matrices with the structures of Toeplitz, Hankel, Vandermonde and Cauchy types are omnipresent in modern computations in Sciences, Engineering and Signal and Image Processing. The four matrix classes have distinct features, but in [P90] we showed that Vandermonde and Hankel multipliers transform all these structures into each other and proposed to employ this property in order to extend any suc...

We reduce several computations with Hilbert and Vandermonde type matrices to matrix computations of the Hankel-Toeplitz type (and vice versa). This unifies various known algorithms for computations with dense structured matrices and enables us to extend any progress in computations with matrices of one class to the computations with other classes of matrices. In particular, this enables us to c...

In this paper we derive a fast O(n) algorithm for solving linear systems where the coefficient matrix is a polynomial-Vandermonde VR(x) = [rj−1(xi)] matrix with polynomials R related to a quasiseparable matrix. The result is a generalization of the well-known Björck-Pereyra algorithm for classical Vandermonde systems. As will be shown, many important systems of polynomials are related to quasis...