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This paper introduces a method for approximately eliminating the effect that conductivity changes outside the region of interest have in electrical impedance tomography, allowing to form a local reconstruction in the region of interest…
Necessary and sufficient conditions are presented for a measure to be the spectral measure of a finite range or exponentially decaying perturbation of a periodic Jacobi operator. As a corollary we can fully solve the inverse resonance…
A previous knowledge of the domains of dependence of an Hamilton Jacobi equation can be useful in its study and approximation. Information of this nature are, in general, difficult to obtain directly from the data of the problem. In this…
Motivated by the increasing availability of high-performance parallel computing, we design a distributed parallel algorithm for linearly-coupled block-structured nonconvex constrained optimization problems. Our algorithm performs…
We consider the problem of embedding eigenvalues into the essential spectrum of periodic Jacobi operators, using an oscillating, decreasing potential. To do this we employ a geometric method, previously used to embed eigenvalues into the…
A systematic investigation of the skew-symmetric solutions of the three-dimensional Jacobi equations is presented. As a result, three disjoint and complementary new families of solutions are characterized. Such families are very general,…
We study operators on rooted graphs with a certain spherical homogeneity. These graphs are called path commuting and allow for a decomposition of the adjacency matrix and the Laplacian into a direct sum of Jacobi matrices which reflect the…
High resolution reconstruction of complicated objects from incomplete and noisy data can be achieved by solving modulation equations iteratively under physical constraints. This direct demodulation method is a powerful technique for dealing…
We consider a periodic Jacobi operator $H$ with finitely supported perturbations on ${\Bbb Z}.$ We solve the inverse resonance problem: we prove that the mapping from finitely supported perturbations to the scattering data: the inverse of…
In this paper, we consider the inverse eigenvalue problem for the positive doubly stochastic matrices, which aims to construct a positive doubly stochastic matrix from the prescribed realizable spectral data. By using the real Schur…
A generalization of the Vandermonde matrices which arise when the power basis is replaced by the Said-Ball basis is considered. When the nodes are inside the interval (0,1), then those matrices are strictly totally positive. An algorithm…
A novel framework for designing image reconstruction algorithms for linear forward problems is proposed. The framework is based on the novel concept of conserving the information in the data during image reconstruction rather than…
This work introduces a method for preprocessing measurements of electrical impedance tomography to considerably reduce the effect uncertainties in the electrode contacts have on the reconstruction quality, without a need to explicitly…
In computer graphics, smooth data reconstruction on 2D or 3D manifolds usually refers to subdivision problems. Such a method is only valid based on dense sample points. The manifold usually needs to be triangulated into meshes (or patches)…
We propose a new joint image reconstruction method by recovering edge directly from observed data. More specifically, we reformulate joint image reconstruction with vectorial total-variation regularization as an $l_1$ minimization problem…
We prove that general three- or four-dimensional systems %of differential equations are real-analytically nonintegrable near degenerate equilibria in the Bogoyavlenskij sense under additional weak conditions when the Jacobian matrices have…
We study the bispectrality of Jacobi type polynomials, which are eigenfunctions of higher-order differential operators and can be defined by taking suitable linear combinations of a fixed number of consecutive Jacobi polynomials. Jacobi…
This paper highlights a formal connection between two families of widely used matrix factorization algorithms in numerical linear algebra. One family consists of the Jacobi eigenvalue algorithm and its variants for computing the Hermitian…
Solving complex optimization problems in engineering and the physical sciences requires repetitive computation of multi-dimensional function derivatives. Commonly, this requires computationally-demanding numerical differentiation such as…
We consider multi-agent, convex optimization programs subject to separable constraints, where the constraint function of each agent involves only its local decision vector, while the decision vectors of all agents are coupled via a common…