In this paper, we study the following extremal problem and its relevance to the sum of the so-called superoptimal singular values of a matrix function: Given an m × n matrix function Φ, when is there a matrix function Ψ * in the set A n,m k such that Z T trace(Φ(ζ)Ψ * (ζ))dm(ζ) = sup Ψ∈A n,m k ˛ ˛ ˛ ˛ Z T trace(Φ(ζ)Ψ(ζ))dm(ζ) ˛ ˛ ˛ ˛ ? The set A n,m k is defined by A n,m k def = n Ψ ∈ H 1 0 (Mn...

for some nonzero vector x called an eigenvector. This is equivalent to writing (λI − A)x = 0 so, since x 6= 0, A− λI must be singular, and hence det(λI − A) = 0. From the (complicated!) definition of determinant, it follows that det(λI−A) is a polynomial in the variable λ with degree n, and this is called the characteristic polynomial. By the fundamental theorem of algebra (a nontrivial result)...

In this paper, for a given matrix [Formula: see text], in terms of [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text], some new inclusion sets for singular values of the matrix are established. It is proved that the new inclusion sets are tighter than the Geršgorin-type sets (Qi in Linear Algebra Appl. 56:105-119, 1984) and the Brauer-type sets (Li in Co...

. We denote by A1(N) and A0(N) the modular function fields with respect to Γ1(N) and Γ0(N) respectively. Let E be a set of triples of integers a = [a1, a2, a3] with the properties 0 < ai ≤ N/2 and ai 6= aj for i 6= j. For an element τ of complex upper half plane H, we denote by Lτ the lattice in C generated by 1 and τ . Let ℘(z;Lτ ) be the Weierstrass ℘-function relative to the lattice Lτ . For...

The paper presents a revised and improved version of a polynomial algorithm published by N. J. Young in 1990 for the Computation of the singular values and vectors of the Hankel operator defined by a linear time-invariant system with rational transfer matrix.

In this paper we study singular values of a matrix whose one entry varies while all other entries are prescribed. In particular, we find the possible pth singular value of such a matrix, and we define explicitly the unknown entry such that the completed matrix has the minimal possible pth singular value. This in turn determines possible pth singular value of a matrix under rank one perturbation...

This paper describes a computational method for improving the accuracy of a given singular value and its associated left and right singular vectors. The method is analogous to iterative improvement for the solution of linear systems. That is, by means of a low-precision computation, an iterative algorithm is applied to increase the accuracy of the singular value and vectors; extended precision ...

In this paper, a steganography technique for JPEG2000 compressed images using singular value decomposition in wavelet transform domain is proposed. In this technique, DWT is applied on the cover image to get wavelet coefficients and SVD is applied on these wavelet coefficients to get the singular values. Then secret data is embedded into these singular values using scaling factor. Different com...

This article presents a new subspace-based technique for reducing the noise of signals in time-series. In the proposed approach, the signal is initially represented as a data matrix. Then using Singular Value Decomposition (SVD), noisy data matrix is divided into signal subspace and noise subspace. In this subspace division, each derivative of the singular values with respect to rank order is u...

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.