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 ...

with σ1 ≥ σ2 ≥ · · · ≥ σr > 0 and r = rank(A). In the above, σ1, . . . , σr are the square roots of the eigenvalues of AA. They are called the singular values of A. Our basic goal is to “solve” the system Ax = b for all matrices A and vectors b. A second goal is to solve the system using a numerically stable algorithm. A third goal is to solve the system in a reasonably efficient manner. For in...

Singular value decomposition is central to many problems in engineering and scientific fields. Several quantum algorithms have been proposed determine the singular values their associated vectors of a given matrix. Although these are promising, required subroutines resources too costly on near-term devices. In this work, we propose variational algorithm for (VQSVD). By exploiting principles Ky ...

abstract The singular value decomposition has a number of applications in digital signal processing. However, the the decomposition must be computed from a matrix consisting of both signal and noise. It is therefore important to be able to assess the eeects of the noise on the singular values and singular vectors | a problem in classical perturbation theory. In this paper we survey the perturba...

The particle size control of drug is one of the most important factors affecting the efficiency of the nano-drug production in confined liquid impinging jets. In the present research, for this investigation the confined liquid impinging jet was used to produce nanoparticles of Carbamazepine. The effects of several parameters such as concentration, solution and anti-solvent flow rate and solvent...