Ruben Airapetyan

Ruben Airapetyan

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.

Ruben Airapetyan

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.