The singular value decomposition of a rectangular data matrix can be used to understand the structure of the data and give insight into the relationships of the row and column factors. For example, the rows linked to the rows might be experimental conditions of temperature and the experimental conditions linked to the columns might pressure. In a biological setting the rows might be linked to t...

This work studies the Generalized Singular Value Thresholding (GSVT) operator Proxg (·), Proxg (B) = argmin X m ∑

Affine rank minimization algorithms typically rely on calculating the gradient of a data error followed by a singular value decomposition at every iteration. Because these two steps are expensive, heuristic approximations are often used to reduce computational burden. To this end, we propose a recovery scheme that merges the two steps with randomized approximations, and as a result, operates on...

Carlo Tomasi Any m n matrix of rank r transforms the unit sphere in Rn into an r-dimensional hyperellipsoid in Rm. For instance, the rank-2 matrix A = 1 p2 264 p3 p3 3 3 1 1 375 (1) transforms the unit circle on the plane into an ellipse embedded in three-dimensional space. Figure 1 shows the map y = Ax : Two diametrically opposite points on the unit circle are mapped into the two endpoints of ...

The speech enhancement techniques are often employed to improve the quality and intelligibility of the noisy speech signals. This paper discusses a novel technique for speech enhancement which is based on Singular Value Decomposition. This implementation utilizes a Genetic Algorithm based optimization method for reducing the effects of environmental noises from the singular vectors as well as t...

in the process of structural analysis we often come to structures that can be analyzed with simpler methods than the standard approaches. for these structures, known as regular structures, the matrices involved are in canonical forms and their eigen-solution can be performed in a simple manner. however, by adding or removing some elements or nodes, such methods cannot be utilized. here, an effi...

The speech enhancement techniques are often employed to improve the quality and intelligibility of the noisy speech signals. This paper discusses a novel technique for speech enhancement which is based on Singular Value Decomposition. This implementation utilizes a Genetic Algorithm based optimization method for reducing the effects of environmental noises from the singular vectors as well as t...

In this paper, we consider some inverse singular value problems for Toeplitz-related matrices. We construct a Toeplitz-plus-Hankel matrix from prescribed singular values including a zero singular value. Then we find a solution to the inverse singular value problem for Toeplitz matrices which have double singular values including a double zero singular value.