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In this paper we study the problem of model reduction by moment matching for stochastic systems. We characterize the mathematical object which generalizes the notion of moment to stochastic differential equations and we find a class of…
This paper deals with (1) the truncated matrix Hamburger moment problem from the point of view of reproducing kernel Hilbert spaces of vector valued entire functions of the kind introduced and extensively studied by Louis de Branges and (2)…
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…
Triangulation of a three-dimensional point from at least two noisy 2-D images can be formulated as a quadratically constrained quadratic program. We propose an algorithm to extract candidate solutions to this problem from its semidefinite…
This paper is about the general truncated matrix-valued moment problem. Let $\mathcal{H}_q$ denote the complex Hermitian $q\times q$-matrices, $q\in \mathbb{N}$. Suppose that $(\mathcal{X},\mathfrak{X})$ is a measurable space and…
Representation of the quantum measurement with the help of non-orthogonal decomposition of unit is presented in the paper for the first time. Methods for solution of the quantum detection and measurement problems based on the suggested…
In this paper, we use the properties of the self-polar triangle to not only show a novel method for a basic point-line enumerative problem of conics, but also present a series of closed-form solutions to the conics from all minimal…
We expose in full detail a constructive procedure to invert the so--called "finite Markov moment problem". The proofs rely on the general theory of Toeplitz matrices together with the classical Newton's relations.
A new approach in solution of simple quantum mechanical problems in deformed space with minimal length is presented. We propose the generalization of Schro\"edinger equation in momentum representation on the case of deformed Heisenberg…
The first part of this paper is devoted to an analysis of moment problems in R^n with supports contained in a closed set defined by finitely many polynomial inequalities. The second part of the paper uses the representation results of…
We establish relationships between the classical moments problems which are problems of a construction of a measure supported on a real line, on a half-line or on an interval from prescribed set of moments with the Boundary control approach…
We assume that a finite set of moments of a random vector is given. Its underlying density is unknown. An algorithm is proposed for efficiently calculating Dirac mixture densities maintaining these moments while providing a homogeneous…
In this article we study the bivariate truncated moment problem (TMP) of degree $2k$ on the union of parallel lines. First we present an alternative proof of Fialkow's solution \cite{Fia15} to the TMP on the union of two parallel lines…
In this paper, we study the truncated matrix moment problem in one variable through recursive matrix extensions. \ We give necessary and sufficient conditions for a recursive matrix extension of finite data to be a matrix moment sequence in…
Given a closed subset $K$ in $\mathbb{R}$, the rational $K$-truncated moment problem ($K$-RTMP) asks to characterize the existence of a positive Borel measure $\mu$, supported on $K$, such that a linear functional $\mathcal{L}$, defined on…
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…
We discuss existence of mixed state of multicomponent system with given spectrum and given reduced density matrices. We give a complete solution of the problem in terms of linear inequalities on the spectra, accompanied with extensive…
The main result of the paper gives criteria for extendibility of sesquilinear form-valued mappings defined on symmetric subsets of *-semigroups to positive definite ones. By specifying this we obtain new solutions of: * the truncated…
A long series of previous papers have been devoted to the (one-dimensional) moment problem with nonnegative rational measure. The rationality assumption is a complexity constraint motivated by applications where a parameterization of the…
We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are…