Linear time-invariant networks are modelled by linear differential-algebraic equations with constant coefficients. These equations can be represented by a matrix pencil. Many publications on this subject are restricted to regular matrix pencils. In particular, the influence of the Weierstrass structure of a regular pencil on the poles of its inverse is well known. In this paper we investigate s...

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...

This chapter is about eigenvalues and singular values of matrices. Computational algorithms and sensitivity to perturbations are both discussed. An eigenvalue and eigenvector of a square matrix A are a scalar λ and a nonzero vector x so that Ax = λx. A singular value and pair of singular vectors of a square or rectangular matrix A are a nonnegative scalar σ and two nonzero vectors u and v so th...

DIAGONAL ELEMENTS, EIGENVALUES, AND SINGULAR VALUES DRAFT AS OF April 30, 2013 SHENG-JHIH WU AND MOODY T. CHU Abstract. Diagonal entries and eigenvalues of a Hermitian matrix, diagonal entries and singular values of a general matrix, and eigenvalues and singular values of a general matrix satisfy necessarily some majorization relationships which turn out also to be sufficient conditions. The in...

In this paper, we consider the singular values and singular vectors of finite, low rank perturbations of large rectangular random matrices. Specifically, we prove almost sure convergence of the extreme singular values and appropriate projections of the corresponding singular vectors of the perturbed matrix. As in the prequel, where we considered the eigenvalues of Hermitian matrices, the non-ra...

this paper undertakes the synthesis of a logic-based switching h2/h∞ state-feedback controller for continuous-time lti singular perturbation systems. our solution achieves a minimum bound on the h2 performance level, while also satisfying the h∞ performance requirements. the proposed hybrid control scheme is based on a fuzzy supervisor managing the combination of two controllers. a convex lmi-b...

Let A 2 R mn be a matrix with known singular values and singular vectors, and let A 0 be the matrix obtained by appending a row to A. We present stable and fast algorithms for computing the singular values and the singular vectors of A 0 in O ? (m + n) min(m;n) log 2 2 oating point operations, where is the machine precision. Previous algorithms can be unstable and compute the singular values an...

In this paper, we show that the SVD of a matrix can be constructed efficiently in a hierarchical approach. Our algorithm is proven to recover the singular values and left singular vectors if the rank of the input matrix A is known. Further, the hierarchical algorithm can be used to recover the d largest singular values and left singular vectors with bounded error. We also show that the proposed...

In this paper, we present a new method for calculating the singular values bounds of an interval matrix. we regard singular values as the the largest eigenvalues of the Jordan-Wielandt matrix. Using the property of eigenvalue bound for interval matrix, we give a method about singular values bounds. This method can analyse stability of systems in control fields extensively. An numerical example ...