Related papers: The Nevanlinna-type formula for the truncated matr…
Let $U$ be a matrix chosen randomly, with respect to Haar measure, from the unitary group $U(d).$ We express the moments of the trace of any submatrix of $U$ as a sum over partitions whose terms count certain standard and semistandard Young…
The present paper is devoted to the {\it local moment problem}, which consists in finding of non-decreasing functions on the real axis having given first $2n+1, \; n\geq 0,$ power moments on the whole axis and also $2m+1$ first power…
Moment methods are classical approaches that approximate the mesoscopic radiative transfer equation by a system of macroscopic moment equations. An expansion in the angular variables transforms the original equation into a system of…
In recent years, the so-called polynomial moment problem, motivated by the classical Poincare center-focus problem, was thoroughly studied, and the answers to the main questions have been found. The study of a similar problem for rational…
In a series of fundamental papers BK Ghosh reduced the simultaneous stabilization problem to a NevanlinnaPick interpolation problem. In this paper we generalize some of these results allowing for derivative constraints. Moreover, we apply a…
Let T be the quasi-nilpotent DT-operator. By use of Voiculescu's amalgamated R-transform we compute the moments of $(T-\lambda 1)^*(T-\lambda 1)$, where $\lambda \in \mathbb C$, and the Brown-measure of $T+\sqrt{\epsilon} Y$, where Y is a…
A new time relaxation model with iterative modified Lavrentiev regularization method is studied. The aim of the relaxation term is to drive the unresolved fluctuations in a computational simulation to zero exponentially faster by an…
We introduce a Julia implementation of the recently proposed Nevanlinna analytic continuation method. The method is based on Nevanlinna interpolants and, by construction, preserves the causality of a response function. For theoretical…
We investigate the generalized moment membership problem for matrices, a formulation equivalent to Skolem's problem for linear recurrence sequences. We show decidability for orthogonal, unitary, and real eigenvalue matrices, and…
This paper is concerned with recovering the solution of a final value problem associated with a parabolic equation involving a non linear source and a non-local term, which to the best of our knowledge has not been studied earlier. It is…
We consider the bifurcation problem $u'' + \lambda u = N(u)$ with two point boundary conditions where $N(u)$ is a general nonlinear term which may also depend on the eigenvalue $\lambda$. We give a variational characterization of the…
In this article we investigate model order reduction of large-scale systems using time-limited balanced truncation, which restricts the well known balanced truncation framework to prescribed finite time intervals. The main emphasis is on…
A numerical technique used to solve boundary value problems is modified to find periodic steady-state solutions of nonautonomous dynamical systems. The technique uses a matrix representation of the time derivative obtained through…
This paper studies global solvability of the Cauchy problem for a generalized time-fractional Kuramoto-Sivashinsky equation in the Shwartz space, which is a complete topological space generated by a family of semi-norms. The main approach…
By using Schur transformed sequences and Dyukarev-Stieltjes parameters we obtain a new representation of the resolvent matrix corresponding to the truncated matricial Stieltjes moment problem. Explicit relations between orthogonal matrix…
The multidimensional moment problem is studied in terms of the Steiltjes transform. The diagonal step-by-step algorithm is constructed for the multidimensional moment problem. The set of solutions of the full multidimensional moment problem…
This paper is concerned with backward problem for nonlinear space fractional diffusion with additive noise on the right-hand side and the final value. To regularize the instable solution, we develop some new regularized method for solving…
The numerical solution of linear discrete ill-posed problems typically requires regularization, i.e., replacement of the available ill-conditioned problem by a nearby better conditioned one. The most popular regularization methods for…
The evaluation of a matrix exponential function is a classic problem of computational linear algebra. Many different methods have been employed for its numerical evaluation [Moler C and van Loan C 1978 SIAM Review 20 4], none of which…
We consider a time fractional differential equation of order $\alpha$, $0<\alpha<1$, $$ \frac{\partial c(x,t)}{\partial t}={}^C_0\mathcal{D}_t^{\alpha}[(Ac)(x,t)]+q(x,t) ,\quad x > 0, t > 0, \quad c(x,0)=f(x). $$ where…