On matrix generalization of Robinson's Energy Delay Theorem
An elementary proof of Robinson's Energy Delay Theorem on minimum-phase functions is presented. The proof is generalized to the matrix case as well.
math.CV↗
arXiv subjects
L. Ephremidze
Publications and source records attributed to L. Ephremidze.
On non-optimal spectral factorizations
For a given Laurent polynomial matrix function $S$, which is positive definite on the unit circle in the complex plane, we consider all possible polynomial spectral factors of $S$ which are not necessarily invertible inside the unit circle.
math.CV↗
On algorithmization of Janashia-Lagvilava matrix spectral factorization method
We consider three different ways of algorithmization of the Janashia-Lagvilava spectral factorization method. The first algorithm is faster than the second one, however, it is only suitable for matrices of low dimension. The second algorithm, on the other hand, can be applied to matrices of substantially larger dimension. The third algorithm is a superfast implementation of the method, but only works in the polynomial case under the additional restriction that the zeros of the determinant are not too close to the boundary. All three algorithms fully utilize the advantage of the method which carries out spectral factorization of leading principal submatrices step-by-step. The corresponding results of numerical simulations are reported in order to describe the characteristic features of each algorithm and compare them to other existing algorithms.
math.NA↗
An Analytic Proof of the Matrix Spectral Factorization Theorem
An analytic proof is proposed of Wiener's theorem on factorization of positive definite matrix-functions.
math.CV↗
A simple proof of the matrix-valued Fejér-Riesz theorem
A very short proof of the Fejér-Riesz lemma is presented in the matrix case
math.CV↗