I. Kurbatova

activity

20142024

most citedAnalytic functional calculus for two operators

5 citations · 6 across the 10 of their papers we have counts for

collaborators

10 papers

math.NA2024

A complete pair of solvents of a quadratic matrix pencil

V. G. Kurbatov, I. V. Kurbatova

Let $B$ and $C$ be square complex matrices. The differential equation \begin{equation*} x''(t)+Bx'(t)+Cx(t)=f(t) \end{equation*} is considered. A solvent is a matrix solution $X$ o…

math.NA2021

An estimate of approximation of an analytic function of a matrix by a rational function

M. Ferus, V. G. Kurbatov, I. V. Kurbatova

Let $A$ be a square complex matrix; $z_{1}$ , ..., $z_{N} \in C$ be arbitrary (possibly repetitive) points of interpolation; $f$ be an analytic function defined on a neighborhoo…

math.NA2021

Calculating a function of a matrix with a real spectrum

P. Kubelík, V. G. Kurbatov, I. V. Kurbatova

Let $T$ be a square matrix with a real spectrum, and let $f$ be an analytic function. The problem of the approximate calculation of $f (T)$ is discussed. Applying the Schur triangul…

math.NA2019

An estimate of Green's function of the problem of bounded solutions in the case of a triangular coefficient

V. G. Kurbatov, I. V. Kurbatova

An estimate of Green's function of the bounded solutions problem for the ordinary differential equation $x^{'} (t) - B x (t) = f (t)$ is proposed. It is assumed that the matrix coefficient $B…

math.NA2018

An estimate of approximation of a matrix-valued function by an interpolation polynomial

V. G. Kurbatov, I. V. Kurbatova

Let $A$ be a square complex matrix, $z_{1}$ , ..., $z_{n} \in C$ be (possibly repetitive) points of interpolation, $f$ be analytic in a neighborhood of the convex hull of the un…

math.FA2018

Green's function of the problem of bounded solutions in the case of a block triangular coefficient

V. G. Kurbatov, I. V. Kurbatova

It is known that the equation $x^{'} (t) = A x (t) + f (t)$ , where $A$ is a bounded linear operator, has a unique bounded solution $x$ for any bounded continuous free term~ $f$ if and only if…

math.FA2017

The Gelfand--Shilov type estimate for Green's function of the bounded solutions problem

V. G. Kurbatov, I. V. Kurbatova

An analog of the Gelfand--Shilov estimate of the matrix exponential is proved for Green's function of the problem of bounded solutions of the ordinary differential equation $x'(t)-…

math.NA2017★ 1 cited

Computation of Green's function of the bounded solutions problem

V. G. Kurbatov, I. V. Kurbatova

It is well known that the equation $x^{'} (t) = A x (t) + f (t)$ , where $A$ is a square matrix, has a unique bounded solution $x$ for any bounded continuous free term $f$ , provided the coeffi…

math.FA2016★ 5 cited

Analytic functional calculus for two operators

V. G. Kurbatov, I. V. Kurbatova, M. N. Oreshina

Properties of the mappings \begin{align*} C&\mapsto\frac1{(2πi)^2}\int_{Γ_1}\int_{Γ_2}f(λ,μ)\,R_{1,\,λ}\,C\, R_{2,\,μ}\,dμ\,dλ, C&\mapsto\frac1{2πi}\int_Γg(λ)R_{1,\,λ}\,C\, R_{2,\,…

math.NA2014

Computation of a function of a matrix with close eigenvalues by means of the Newton interpolating polynomial

V. G. Kurbatov, I. V. Kurbatova

An algorithm for computing an analytic function of a matrix $A$ is described. The algorithm is intended for the case where $A$ has some close eigenvalues, and clusters (subsets) of…