The linear system of equations Ax = b where A = [aij ] in Cn.n is a crispsingular matrix and the right-hand side is a fuzzy vector is called a singularfuzzy linear system of equations. In this paper, solving singular fuzzy linearsystems of equations using generalized inverses such as Drazin inverse andpseudo-inverse are investigated.

We consider a two-tile reconfigurable intelligent surface (RIS) assisted wireless network with two-antenna transmitter and receiver over Rayleigh fading. show that the average received signal-to-noise-ratio (SNR) optimal combining transmission vectors are given by left right singular spaces of RIS-receiver transmit-RIS channel matrices, respectively. Moreover, phases at two tiles RIS determined...

Abstract This contribution presents a proper generalized decomposition-based nonlinear solver for an efficient solution of geometrically dynamic problems. The is built as sum dyadic products space and time modes, this so-called enrichments truncated when the required accuracy achieved. In proposed algorithm, we apply consistent linearization residual vectors around currently known over whole sp...

Explicit expressions for the singular vectors in the highest weight representations of A (1) 1 are obtained using the fusion formalism of conformal field theory.

In this study, we consider a sampling-type algorithm for the fast localization of small electromagnetic inhomogeneities from measured far-field pattern data in limited-aperture inverse scattering problem. For purpose, designed an indicator function based on structure left- and right-singular vectors multistatic response matrix, elements which were data. We then rigorously investigated mathemati...

We show how the interplay between the fusion formalism of conformal field theory and the Knizhnik–Zamolodchikov equation leads to explicit formulae for the singular vectors in the highest weight representations of A (1) 1. Infinite dimensional Lie algebras occur everywhere in the study of 2-d conformal field theories: the Virasoro algebra and the affine algebras are the most common examples. Ho...

We present a parallel software implementation for computing the singular value decomposition (SVD) of general, banded or bidiagonal matrices. First, the matrix is reduced to bidiagonal form. This reduction can be rearranged in a way that allows heavy use of matrix-matrix operations. Then the singular values are computed in an iterative process. Finally the singular vectors are computed independ...