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...

In this paper, we consider large-scale linear discrete ill-posed problems where the right-hand side contains noise. Regularization techniques such as Tikhonov regularization are needed to control the effect of the noise on the solution. In many applications such as in image restoration the coefficient matrix is given as a Kronecker product of two matrices and then Tikhonov regularization proble...

The paper deals with the minimum case where the order of the observer and the number of observed variables are equal. The results are deduced from the analysis of the necessary and sufficient existence conditions for an asymptotic observer. A constructive procedure for the design of a minimum linear functional observer for a linear time-varying linear system is given. As a specific feature, the...

We introduce Gaussian Process Topic Models (GPTMs), a new family of topic models which can leverage a kernel among documents while extracting correlated topics. GPTMs can be considered a systematic generalization of the Correlated Topic Models (CTMs) using ideas from Gaussian Process (GP) based embedding. Since GPTMs work with both a topic covariance matrix and a document kernel matrix, learnin...

In this talk we extend the concept of the convex scattering support to the case of electrostatics in a bounded domain. Furthermore, we apply this approach to devise a new reconstruction algorithm in electric impedance tomography. The convex scattering support was developed by Stephen Kusiak and John Sylvester, cf. [3],[4], and is meant to be the smallest convex set that contains a scattering so...

A novel state-space realization for parametric macromodeling is proposed in this paper. A judicious choice of the state-space realization is required to account for the generally assumed smoothness of the state-space matrices with respect to the design parameters. This is used in combination with suitable interpolation schemes to interpolate a set of state-space matrices, and hence the poles an...

The solution to a general Sylvester equation AX − XB = GF with a low-rank right-hand side is analyzed quantitatively through the Low-rank Alternating-Directional-Implicit method (LR-ADI) with exact shifts. New bounds and perturbation bounds on X are obtained. A distinguished feature of these bounds is that they reflect the interplay between the eigenvalue decompositions of A and B and the right...

We present a unifying computational framework to solve robust pole assignment problems for linear systems using state feedback. The new framework uses Sylvester equation based parametrizations of the pole assignment problems. The non-uniqueness of solutions is exploited by minimizing additionally sensitivity of closed-loop eigenvalues and the norm of the corresponding state feedback matrix. The...

By using a generalized Sylvester equation based parametrization, three minimum norm robust pole assignment problems for descriptor systems are formulated as unconstrained minimization problems for suitably chosen cost functions. The derived explicit expressions of the gradients of the cost functions allow the efficient solution of the minimization problems by using powerful gradient search base...

If G and H are two cubic graphs, then an H-coloring of G is a proper edge-coloring f with edges of H , such that for each vertex x of G, there is a vertex y of H with f(∂G(x)) = ∂H(y). If G admits an H-coloring, then we will write H ≺ G. The Petersen coloring conjecture of Jaeger states that for any bridgeless cubic graph G, one has: P ≺ G. The second author has recently introduced the Sylveste...