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In this paper, we consider a general discrete-time spectral factorization problem for rational matrix-valued functions. We build on a recent result establishing existence of a spectral factor whose zeroes and poles lie in any pair of…
A new method of matrix spectral factorization is proposed which reliably computes an approximate spectral factor of any matrix spectral density that admits spectral factorization
Factor analysis refers to a statistical model in which observed variables are conditionally independent given fewer hidden variables, known as factors, and all the random variables follow a multivariate normal distribution. The parameter…
Though there have been hundreds of methods on solving rational spectral factorization, most of them are based on a positive definite density matrix assumption. In this work, we propose a novel approach on the spectral factorization of a…
We formulate a conjecture concerning spectral factorization of a class of trigonometric polynomials of two variables and prove it for special cases. Our method uses relations between the distribution of values of a polynomial of two…
This paper considers a restriction to non-negative matrix factorization in which at least one matrix factor is stochastic. That is, the elements of the matrix factors are non-negative and the columns of one matrix factor sum to 1. This…
A factor of a graph is a spanning subgraph. Spectral sufficient conditions are provided via spectral radius and signless Laplacian spectral radius for graphs with (i) a matching of given size (particularly, $1$-factor) containing any given…
This paper contains a re-evaluation of the spectral approach and factorizability for regular matrix polynomials. In addition, solvent theory is extended from the monic and comonic cases to the regular case. The classification of extended…
In this paper, we investigate Bauer's method for the matrix spectral factorization of an r-channel matrix product filter which is a halfband autocorrelation matrix. We regularize the resulting matrix spectral factors by an averaging…
In this paper we factorize matrix polynomials into a complete set of spectral factors using a new design algorithm and we provide a complete set of block roots (solvents). The procedure is an extension of the (scalar) Horner method for the…
In light of recent data science trends, new interest has fallen in alternative matrix factorizations. By this, we mean various ways of factorizing particular data matrices so that the factors have special properties and reveal insights into…
We study conditions under which a partial differential operator of arbitrary order $n$ in two variables or ordinary linear differential operator admits a factorization with a first-order factor on the left. The factorization process…
This paper concerns some spectral properties of the scalar dynamical system defined by a linear delay-differential equation with two positive delays. More precisely, the existing links between the delays and the maximal multiplicity of the…
We sketch the history of spectral ranking, a general umbrella name for techniques that apply the theory of linear maps (in particular, eigenvalues and eigenvectors) to matrices that do not represent geometric transformations, but rather…
A spectral factorization theorem is proved for polynomial rank-deficient matrix-functions. The theorem is used to construct paraunitary matrix-functions with first rows given.
The dynamical symmetries of the Kratzer-type molecular potentials (generalized Kratzer molecular potentials) are studied by using the factorization method. The creation and annihilation (ladder) operators for the radial eigenfunctions…
This paper investigates spectral properties of certain classes of positive operators originated from different matrices appeared in linear complementarity problem. These positive operators play a crucial role in various areas of mathematics…
Prior to the parallel solution of a large linear system, it is required to perform a partitioning of its equations/unknowns. Standard partitioning algorithms are designed using the considerations of the efficiency of the parallel…
We describe a seriation algorithm for ranking a set of items given pairwise comparisons between these items. Intuitively, the algorithm assigns similar rankings to items that compare similarly with all others. It does so by constructing a…
We give three algebraic equations which allow a geometric classification of all spectral types of equilibria of a given $m$-dimensional dynamical system, and we analyse them thoroughly in dimension 3 and 4. The loci defined by these…