arXiv subjects

Ruben Airapetyan

Publications and source records attributed to Ruben Airapetyan.

3 recordsLinked to original sources

arXiv2026

A layer stripping method for numerical solution of the GPR problem in a layered medium

A numerical method for processing the data of ground penetrating radars for a piece-wise continuous layered medium is proposed. The method combines the layer stripping technique with numerical continuation of data into the complex frequency's domain. The accuracy of the method is analyzed. Error estimates are obtained and numerical testing is performed. They demonstrate numerical efficiency of the method under certain assumptions such as: electrical characteristics inside each layer change slowly, the thicknesses of the layers are at least of the order of the wavelength, conductivity of the medium is not high.

math.NA↗

arXiv2025

On the Method of Partial Fractions with Matrix Coefficients and Applications

The paper introduces a method of partial fractions with matrix coefficients and its applications to finding chains of generalized eigenvectors, to evaluation of matrix exponentials, and to solution of linear systems of ordinary differential equations with constant coefficients.

math.CA↗

arXiv2012

On principal minors of Bezout matrix

Let $x_1,...,x_{n}$ be real numbers, $P(x)=p_n(x-x_1)...(x-x_n)$, and $Q(x)$ be a polynomial of degree less than or equal to $n$. Denote by $Δ(Q)$ the matrix of generalized divided differences of $Q(x)$ with nodes $x_1,...,x_n$ and by $B(P,Q)$ the Bezout matrix (Bezoutiant) of $P$ and $Q$. A relationship between the corresponding principal minors, counted from the right-hand lower corner, of the matrices $B(P,Q)$ and $Δ(Q)$ is established. It implies that if the principal minors of the matrix of divided differences of a function $g(x)$ are positive or have alternating signs then the roots of the Newton's interpolation polynomial of $g$ are real and separated by the nodes of interpolation.

math.NA↗