We discuss extended definitions of linear and multilinear operations such as Kronecker, Hadamard, and contracted products, and establish links between them for tensor calculus. Then we introduce effective low-rank tensor approximation techniques including Candecomp/Parafac (CP), Tucker, and tensor train (TT) decompositions with a number of mathematical and graphical representations. We also pro...

Decomposition of mixed information into its constituent components has been very useful in many applications such as acoustics, communications, and biomedicine. Eigenvalue decomposition (EVD), singular value decomposition (SVD), and independent component analysis (ICA) based on various criteria such as uncorrelatedness, independency, minimizing mutual information, and differences in distributio...

Polarimetric decomposition techniques and inversion algorithms are developed and applied on the OPAQUE data set acquired in spring 2007 to investigate their potential and limitations for soil moisture estimation. A three component model-based decomposition is used together with an eigenvalue decomposition in a combined approach to invert for soil moisture over bare and vegetated soils at L-band...

Fluid queueing models with finite capacity buffers are applied to analyze a wide range of real life systems. There are well established numerical procedures for the analysis of these queueing models when the load is lower or higher than the system capacity, but these numerical methods become unstable as the load gets close to the system capacity. One of the available numerical procedures is the...

The generalized null space decomposition (GNSD) is a unitary reduction of a general matrix A of order n to a block upper triangular form that reveals the structure of the Jordan blocks of A corresponding to a zero eigenvalue. The reduction was introduced by Kublanovskaya. It was extended first by Ruhe and then by Golub and Wilkinson, who based the reduction on the singular value decomposition. ...

In this paper, an angle of arrival (AOA) estimator is presented. Accurate AOA estimation is very crucial for many applications such as wireless positioning and signal enhancement using space processing techniques. The proposed estimator is based upon applying the eigenvalue decomposition (EVD) method on the crosscorrelation matrix of the received signals at two sides of the antenna array double...

The paper addresses the discrete-time linear process identification problem assuming noisy input and output records available for the parameter estimation. The efficient algorithms are derived for the simultaneous estimation of the process and noise parameters. Implementation techniques based on matrix and polynomial decompositions are given in details resulting in estimation algorithms with re...

This correspondence investigates the gain in statistical performance/complexity of the adaptive estimation of the eigenvalue decomposition (EVD) of covariance matrices when the centrosymmetric (CS) structure of such matrices is utilized. After deriving the asymptotic distribution of the EVD estimators, it is shown, in particular, that the closed-form expressions for the asymptotic covariance of...