Let M(A) denote the comparison matrix of a square H-matrix A, that is, M(A) is an M-matrix. Hmatrices such that their comparison matrices are non-singular are well studied in the literature. In this paper, we study characterizations of H-matrices with either singular or non-singular comparison matrices. The spectral radius of the Jacobi matrix of M(A) and the generalized diagonal dominance prop...

Motivated by the definition of P†-matrix ([9]), another generalization of a P -matrix for square singular matrices called PD-matrix is proposed first. Then the uniqueness of solution of Linear Complementarity Problems for square singular matrices is proved using PD-matrices. Finally some results which are true for P -matrices are extended to PD-matrices.

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.

We show that the problem of finding a singular value decomposition of a matrix in the extended max algebra can be reformulated as an Extended Linear Complementarity Problem. This allows us to compute all the max-algebraic singular value decompositions of a matrix. This technique can also be used to calculate many other max-algebraic matrix decompositions.

Here, we will consider one approach for extending the ideas underlying the least-squares algorithm we discussed in class to non-tall matrices. Let A ∈ Rn×d matrix, where both n and d are large, and where rank(A) = k exactly, and let B ∈ Rn×t. Consider the problem minX∈Rn×t‖AX −B‖, where ‖ · ‖ is a unitarily-invariant matrix norm. The solution to this problem is Xopt = AB, and here we consider a...

Matrix completion algorithms recover a low rank matrix from a small fraction of the entries, each entry contaminated with additive errors. In practice, the singular vectors and singular values of the low rank matrix play a pivotal role for statistical analyses and inferences. This paper proposes and studies estimators of these quantities. When the dimensions of the matrix increase to infinity a...

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...

In this report, we present a method for calculating maximum singular value of an interval matrix. First, we provide an algorithm for calculating the maximum singular value of a square interval matrix. Then, based on this algorithm, we extend the result to non-square interval matrix case. Through numerical examples, the validity of the suggested method is illustrated.

We compute the singular points of a plane rational curve, parametrically given, using the implicitization matrix derived from the μ-basis of the curve. It is shown that singularity factors, which are defined and uniquely determined by the elementary divisors of the implicitization matrix, contain all the information about the singular points, such as the parameter values of the singular points ...

This paper presents an O(n2 log n) algorithm for computing the symmetric singular value decomposition of square Hankel matrices of order n, in contrast with existing O(n3) SVD algorithms. The algorithm consists of two stages: first, a complex square Hankel matrix is reduced to a complex symmetric tridiagonal matrix using the block Lanczos method in O(n2 log n) flops; second, the singular values...