Related papers: Inverse eigenproblems and approximation problems f…
In this paper, we consider optimal low-rank regularized inverse matrix approximations and their applications to inverse problems. We give an explicit solution to a generalized rank-constrained regularized inverse approximation problem,…
The language of Lagrangian submanifolds is used to extend a geometric characterization of the inverse problem of the calculus of variations on tangent bundles to regular Lie algebroids. Since not all closed sections are locally exact on Lie…
Call an $n$-by-$n$ invertible matrix $S$ a \emph{Perron similarity} if there is a real non-scalar diagonal matrix $D$ such that $S D S^{-1}$ is entrywise nonnegative. We give two characterizations of Perron similarities and study the…
We discuss two generalizations of the inverse problem of the calculus of variations, one in which a given mechanical system can be brought into the form of Lagrangian equations with non-conservative forces of a generalized Rayleigh…
The efficient inversion of matrix polynomials is a critical challenge in computational mathematics. We design a procedure to determine the inverse of matrices polynomial of multidimensional Laplace matrices. The method is based on…
We study the transference through finite index extensions of the notion of equational coherence, as well as its effective counterpart. We deduce an explicit algorithm for solving the following algorithmic problem about size two integral…
We prove that the inverse of a positive-definite matrix can be approximated by a weighted-sum of a small number of matrix exponentials. Combining this with a previous result [OSV12], we establish an equivalence between matrix inversion and…
The main of this work is to use the unit lower triangular matrices for solving inverse eigenvalue problem of nonnegative matrices and present the easier method to solve this problem.
We introduce a new multivariate statistical problem that we refer to as the Ensemble Inverse Problem (EIP). The aim of EIP is to invert for an ensemble that is distributed according to the pushforward of a prior under a forward process. In…
Let $F(z)=z-H(z)$ with $o(H(z))\geq 2$ be a formal map from $\bC^n$ to $\bC^n$ and $G(z)$ the formal inverse of $F(z)$. In this paper, we fist study the deformation $F_t(z)=z-tH(z)$ and its formal inverse map $G_t(z)$. We then derive two…
Matrices are typically considered over fields or rings. Motivated by applications in parametric differential equations and data-driven modeling, we suggest to study matrices with entries from a Hilbert space and present an elementary theory…
In this note, we investigate Jacobian conjecture through investigation of automorphisms of polynomial rings in characteristic $p$. Making use of the technique of inverse limits, we show that under Jacobian condition for a given homomorphism…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
The problems we address in this paper are the spectral theory and the inverse problems associated with Laplacians on non-compact Riemannian manifolds and more general manifolds admitting conic singularities. In particular, we study the…
We consider the inverse eigenvalue problem for entanglement witnesses, which asks for a characterization of their possible spectra (or equivalently, of the possible spectra resulting from positive linear maps of matrices). We completely…
We say that a list of complex numbers is "realisable" if it is the spectrum of some (entrywise) nonnegative matrix. The Nonnegative Inverse Eigenvalue Problem (NIEP) is the problem of characterising all realisable lists. Although the NIEP…
A tensor $\mathcal T\in \mathbb T(\mathbb C^n,m+1)$, the space of tensors of order $m+1$ and dimension $n$ with complex entries, has $nm^{n-1}$ eigenvalues (counted with algebraic multiplicities). The inverse eigenvalue problem for tensors…
Given a reflection group $G$ acting on a complex vector space $V$, a reflection map is the composition of an embedding $X \hookrightarrow V$ with the orbit map $V\to\mathbb C^p$ that maps a $G$-orbit to a point. Reflection maps can be very…
We present a general framework to study uniqueness, stability and reconstruction for infinite-dimensional inverse problems when only a finite-dimensional approximation of the measurements is available. For a large class of inverse problems…
In this paper, we bring together four different branches of antiholomorphic dynamics: of global anti-rational maps, reflection groups, Schwarz reflections in quadrature domains, and antiholomorphic correspondences. We establish the first…