In this paper, we propose a general method to obtain Linearly Independent NonOrthogonal yet Energy (square of the norm) Preserving (LINOEP) vectors using iterative filtering operation and we refer it as Filter Mode Decomposition (FDM). We show that the general energy preserving theorem (EPT), which is valid for both linearly independent (orthogonal and nonorthogonal) and linearly dependent vect...

This paper presents a two-part decomposition of a spatial filter having to optimize the reception of a useful signal in the presence of an important co-channel interference level. The decomposition highlights the role of two parts of the filter, one devoted to the maximization of the signal to noise ratio and the other devoted to the interference cancellation. The two-part decomposition is used...

In this article, we address the problem of singular value decomposition of polynomial matrices and eigenvalue decomposition of para-Hermitian matrices. Discrete Fourier transform enables us to propose a new algorithm based on uniform sampling of polynomial matrices in frequency domain. This formulation of polynomial matrix decomposition allows for controlling spectral properties of the decompos...

Scales in RNA, based on geometrical considerations, can be exploited for the analysis and prediction of RNA structures. By using spectral decomposition, geometric information that relates to a given RNA fold can be reduced to a single positive scalar number, the second eigenvalue of the Laplacian matrix corresponding to the tree-graph representation of the RNA secondary structure. Along with th...

In this paper are presented current achievements and the state-of-the-art algorithms and implementations for dense linear algebra on traditional architectures such as single-core machines or distributed memory parallel machines. Also, this paper summarizes the current implementations and publicly available libraries for basic linear algebra for multi-core and many-core architectures (e.g. graph...

Limited memory quasi-Newton methods and trust-region methods represent two efficient approaches used for solving unconstrained optimization problems. A straightforward combination of them deteriorates the efficiency of the former approach, especially in the case of large-scale problems. For this reason, the limited memory methods are usually combined with a line search. We show how to efficient...

Abstract. Momentum-space representation renders an interesting perspective to theory of large fluctuations in populations undergoing Markovian stochastic gain-loss processes. This representation is obtained when the master equation for the probability distribution of the population size is transformed into an evolution equation for the probability generating function. Spectral decomposition the...

The spectral properties of the adjacency matrix, in particular its largest eigenvalue and the associated principal eigenvector, dominate many structural and dynamical properties of complex networks. Here we focus on the localization properties of the principal eigenvector in real networks. We show that in most cases it is either localized on the star defined by the node with largest degree (hub...