It is widely known that the solutions of Lyapunov equations can be used to compute the H2 norm of linear timeinvariant (LTI) dynamical systems. In this paper, we show how this theory extends to dynamical systems with delays. The first result is that the H2 norm can be computed from the solution of a generalization of the Lyapunov equation, which is known as the delay Lyapunov equation. From the...

It is widely known that the solutions of Lyapunov equations can be used to compute the H2 norm of linear timeinvariant (LTI) dynamical systems. In this paper, we show how this theory extends to dynamical systems with delays. The first result is that the H2 norm can be computed from the solution of a generalization of the Lyapunov equation, which is known as the delay Lyapunov equation. From the...

We consider a class of matrix spectral norm approximation problems for finding an affine combination of given matrices having the minimal spectral norm subject to some prescribed linear equality and inequality constraints. These problems arise often in numerical algebra, engineering and other areas, such as finding Chebyshev polynomials of matrices and fastest mixing Markov chain models. Based ...

The näıve Nyström extension forms a low-rank approximation to a positive-semidefinite matrix by uniformly randomly sampling from its columns. This paper provides the first relativeerror bound on the spectral norm error incurred in this process. This bound follows from a natural connection between the Nyström extension and the column subset selection problem. The main tool is a matrix Chernoff b...

Current research proposes a natural environment for the space-time codes and in this context it is obtained a new design criterion for space-time codes in multi-antenna communication channels. The objective of this criterion is to minimize the pairwise error probability of the maximum likelihood decoder, endowed with the matrix spectrum norm. The random matrix theory is used and an approximatio...

A speech enhancement method employing sparse reconstruction of the power spectral density is proposed. The overcomplete dictionary of the power spectral density is learned by approximation K-singular value decomposition algorithm with non negative constraint. The power spectral density of clean speech signal is reconstructed by least angle regression method with a norm termination rule, and the...

This paper presents a comparative study of high resolution spectral estimation methods applied to Radar Altimeter. Spectral estimation methods such as Yule-Walker, Burg, Covariance, modified Covariance, MUSIC, minimum norm, ESPRIT methods are briefly reviewed. Computer simulations have been made using a test signal with six frequencies in order to evaluate the probability of detection of each f...

Kernel methods are an extremely popular set of techniques used for many important machine learning and data analysis applications. In addition to having good practical performance, these methods are supported by a well-developed theory. Kernel methods use an implicit mapping of the input data into a high dimensional feature space defined by a kernel function, i.e., a function returning the inne...