The computation of a singular value decomposition of an m× n matrix A is certainly one of the most often demanded tasks in various applications. There are many algorithms for computing the full or partial singular value decomposition. Among them, the one-sided Jacobi method (coupled with some orderings) is reputable for its ability to compute the singular values as well as left and right singul...

The theory of diophantine approximation studies how well x = (x1, . . . , xn) ∈ R can be approximated by (p1/q1, . . . , pn/qn) ∈ Q of a given ‘complexity’, where this complexity is usually measured by the quantity lcm(q1, . . . , qn). Thus one is interested in minimizing the difference, in a suitable sense, between qx and a vector p, where p ∈ Z and q ∈ N, with a given upper bound on q. Often ...

In 1998 the Adapted Ordering Method was developed for the representation theory of the superconformal algebras in two dimensions. It allows: to determine maximal dimensions for a given type of space of singular vectors, to identify all singular vectors by only a few coefficients, to spot subsingular vectors and to set the basis for constructing embedding diagrams. In this article we present the...

Some stochastic evolutions of conformal maps can be described by SLE and may be linked to conformal field theory via stochastic differential equations and singular vectors in highest-weight modules of the Virasoro algebra. Here we discuss how this may be extended to superconformal maps of N = 1 superspace with links to superconformal field theory and singular vectors of the N = 1 superconformal...

Mobile Ad-hoc Networks (MANETs) by contrast of other networks have more vulnerability because of having nature properties such as dynamic topology and no infrastructure. Therefore, a considerable challenge for these networks, is a method expansion that to be able to specify anomalies with high accuracy at network dynamic topology alternation. In this paper, two methods proposed for dynamic anom...

Given a matrix A, it can be shown that there is a vector z ∈ 0, 1 for which |Az|/|Z| ≥ |A|2/C log(n) (a0/1 sum of columns of A which witnesses its large spectral norm) for instance by discretizing the top singular vector of A and taking a dyadic expansion. We give a simple geometric proof of this fact by relating it to the Euclidean diameter of a polytope, and obtain a sharp bound of |Az| ≥ 2|A...

In this work we propose an orthogonal pulse waveform for wireless ultra wideband (UWB) transmission. The design is based on an ideal low-pass prototype filter having a windowed sinc impulse response. The frequency response of the prototype filter is transferred to the high frequency region using a specific sign modulator. The UWB pulse waveform comprises of the weighted summation of the left si...

This paper proposes the use of subspace tracking algorithms for performing MIMO channel estimation at millimeter wave (mmWave) frequencies. Using a subspace approach, we develop a protocol enabling the estimation of the right (resp. left) singular vectors at the transmitter (resp. receiver) side; then, we adapt the projection approximation subspace tracking with deflation (PASTd) and the orthog...

The dynamics of the growth of linear disturbances to a chaotic basic state is analyzed in an asymptotic model of weakly nonlinear, baroclinic wave-mean interaction. In this model, an ordinary differential equation for the wave amplitude is coupled to a partial differential equation for the zonal flow correction. The leading Lyapunov vector is nearly parallel to the leading Floquet vector φ1 of ...

Let a singular value of a bidiagonal matrix be known. Then the corresponding singular vector can be computed through the twisted factorization of a tridiagonal matrix by the discrete Lotka-Volterra with variable step-size (dLVv) transformation. Errors of the singular value then sensitively affect the conditional number of the tridiagonal matrix. In this paper, we first examine a relationship be...