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...

It has been known for some time that the (1, 3) perturbations of the (2k + 1, 2) Virasoro minimal models have conserved currents which are also singular vectors of the Virasoro algebra. This also turns out to hold for the (1, 2) perturbation of the (3k± 1, 3) models. In this paper we investigate the requirement that a perturbation of an extended conformal field theory has conserved currents whi...

This paper presents an O(n2) method based on the twisted factorization for computing the Takagi vectors of an n-by-n complex symmetric tridiagonal matrix with known singular values. Since the singular values can be obtained in O(n2) flops, the total cost of symmetric singular value decomposition or the Takagi factorization is O(n2) flops. An analysis shows the accuracy and orthogonality of Taka...

A procedure for determining determining a few of the largest singular values and corresponding singular vectors of large sparse matrices is presented. Equivalent eigensystems are solved using a technique originally proposed by Golub and Kent based on the computation of modiied moments. The asynchronicity in the computations of moments and eigenvalues makes this method attractive for parallel im...

As illustrated via numerical experiments with an implementation in Spark (the popular platform for distributed computation), randomized algorithms provide solutions to two ubiquitous problems: (1) the distributed calculation of a full principal component analysis or singular value decomposition of a highly rectangular matrix, and (2) the distributed calculation of a low-rank approximation (in t...

A new star pattern recognition method is developed using singular value decomposition of a measured unit column vector matrix in a measurement frame and the corresponding cataloged vector matrix in a reference frame. It is shown that singular values and right singular vectors are invariant with respect to coordinate transformation and robust under uncertainty. One advantage of singular value co...

In conventional binaural rendering a pair of head-related impulse responses (HRIR), measured from source direction to left and right ears, is convolved with a source signal to create the impression of a virtual 3D sound source when played on headphones. It is well known that using HRIRs measured in a real room, which includes a natural reverberant decay, increases the externalization and realis...

The singular vectors of a chemical transport model are the directions of maximum perturbation growth over a finite time interval. They have proved useful for the estimation of error growth, the initialization of ensemble forecasts, and the optimal placement of adaptive observations. The aim of this paper is to address computational aspects of singular vector analysis for atmospheric chemical tr...

HAMID HASSANPOUR School of Information Technology and Computer Engineering, Shahrood University of Technology. ___________________________________________________________________________________ Abstract: In this paper, a new method is presented for noise reduction in signal using partial differential equations. In this approach, the signal is initially represented as a matrix. Then using singu...

High resolution range profile (HRRP) plays an important role in wideband radar automatic target recognition (ATR). In order to alleviate the sensitivity to clutter and target aspect, employing a sequence of HRRP is a promising approach to enhance the ATR performance. In this paper, a novel HRRP sequence-matching method based on singular value decomposition (SVD) is proposed. First, the HRRP seq...