Related papers: The linear request problem
A new algorithm is presented for computing a direct solution to a system of consistent linear equations. It produces a minimum norm particular solution, a generalized inverse (of type {124}), and a null space projection operator. In…
In linear inverse problems, we have data derived from a noisy linear transformation of some unknown parameters, and we wish to estimate these unknowns from the data. Separable inverse problems are a powerful generalization in which the…
In classical continuum theory, Volterra's principle [1, 2] is a long-known method to solve linear rheological (viscoelastic) problems derived from the corresponding elastic ones. Here, we introduce and present another approach that is…
We demonstrate a data-driven method to solve for the invariant probability density function of a randomly perturbed dynamical system. The key idea is to replace the boundary condition of numerical schemes by a least squares problem…
The existence of global-in-time classical solutions to the Cauchy problem of incompressible Magnetohydrodynamic flows with zero magnetic diffusivity is considered in two dimensions. The linearization of equations is a degenerated…
When a solution to an abstract inverse linear problem on Hilbert space is approximable by finite linear combinations of vectors from the cyclic subspace associated with the datum and with the linear operator of the problem, the solution is…
Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…
This paper considers the inversion of ill-posed linear operators. To regularise the problem the solution is enforced to lie in a non-convex subset. Theoretical properties for the stable inversion are derived and an iterative algorithm akin…
This paper is concerned with the Riemann problem for the two-dimensional barotropic compressible Euler system with a general strictly increasing pressure law. By means of convex integration, the existence of infinitely many admissible weak…
We show continuity in generalized weighted Morrey spaces of sub-linear integral operators generated by some classical integral operators and commutators. The obtained estimates are used to study global regularity of the solution of the…
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…
We provide very mild sufficient conditions for space-time domains (non-necessarily cylindrical) which ensure that the continuous Dirichlet problem and the H\"older Dirichlet problem are well-posed, for any parabolic operator in divergence…
We study a general contracting problem between the principal and a finite set of competitive agents, who perform equivalent changes of measure by controlling the drift of the output process and the compensator of its associated jump…
We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind…
This paper proposes a method to design an optimal dynamic contract between a principal and an agent, who has the authority to control both the principal's revenue and an engineered system. The key characteristic of our problem setting is…
We introduce a new technique for solving uni-parametric versions of linear programs, convex quadratic programs, and linear complementarity problems in which a single parameter is permitted to be present in any of the input data. We…
We consider the problem of equilibration of a single oscillator system with dynamics given by the generalized Langevin equation. It is well-known that this dynamics can be obtained if one considers a model where the single oscillator is…
The Stable Roommates problem involves matching a set of agents into pairs based on the agents' strict ordinal preference lists. The matching must be stable, meaning that no two agents strictly prefer each other to their assigned partners. A…
In this paper, we extend the concept of generalized entropy to uniform spaces, allowing computations beyond metrizable settings. We apply this to parabolic dynamics - systems with a unique fixed point uniformly attracting all compact…
Time-invariant linear dynamical system arises in many real-world applications,and its usefulness is widely acknowledged. A practical limitation with this model is that its latent dimension that has a large impact on the model capability…