Related papers: Interpolating between Tikhonov regularization and …
We consider the identification of scattering and absorption rates in the stationary radiative transfer equation. For a stable solution of this parameter identification problem, we consider Tikhonov regularization within Banach spaces. A…
In this paper, we are concerned with efficiently solving the sequences of regularized linear least squares problems associated with employing Tikhonov-type regularization with regularization operators designed to enforce edge recovery. An…
Tikhonov regularization for projected solutions of large-scale ill-posed problems is considered. The Golub-Kahan iterative bidiagonalization is used to project the problem onto a subspace and regularization then applied to find a subspace…
Operator inference learns low-dimensional dynamical-system models with polynomial nonlinear terms from trajectories of high-dimensional physical systems (non-intrusive model reduction). This work focuses on the large class of physical…
We study refinements between spectral resolutions in an arbitrary II$_1$ factor $\M$ and obtain diffuse (maximal) refinements of spectral resolutions. We construct models of operators with respect to diffuse spectral resolutions. As an…
This paper presents a model reduction method for the class of linear quantum stochastic systems often encountered in quantum optics and their related fields. The approach is proposed on the basis of an interpolatory projection ensuring that…
Variational regularization and the quasisolutions method are justified for unbounded closed, possibly nonlinear, operators. The argument is quite simple and yields general results.
We study Tikhonov regularization for certain classes of non-linear ill-posed operator equations in Hilbert space. Emphasis is on the case where the solution smoothness fails to have a finite penalty value, as in the preceding study…
The joint bidiagonalization process of a matrix pair $\{A,L\}$ can be used to develop iterative regularization algorithms for large scale ill-posed problems in general-form Tikhonov regularization…
In this note, we solve an inverse spectral problem for a class of finite band symmetric matrices. We provide necessary and sufficient conditions for a matrix valued function to be a spectral function of the operator corresponding to a…
The capacitance of capacitive energy storage devices can not be directly measured, but can be estimated from the input and output signals expressed in the time or frequency domains. Here the time-domain voltage-charge relationship in…
Neural integral equations are deep learning models based on the theory of integral equations, where the model consists of an integral operator and the corresponding equation (of the second kind) which is learned through an optimization…
Both structured componentwise and structured normwise perturbation analysis of the Tikhonov regularization are presented. The structured matrices under consideration include: Toeplitz, Hankel, Vandermonde, and Cauchy matrices. Structured…
Operator cutoff regularization based on the original Schwinger's proper-time formalism is examined. By constructing a regulating smearing function for the proper-time integration, we show how this regularization scheme simulates the usual…
For the solution of full-rank ill-posed linear systems a new approach based on the Arnoldi algorithm is presented. Working with regularized systems, the method theoretically reconstructs the true solution by means of the computation of a…
In this paper we discuss a deterministic form of ensemble Kalman inversion as a regularization method for linear inverse problems. By interpreting ensemble Kalman inversion as a low-rank approximation of Tikhonov regularization, we are able…
In this work we consider robust stabilization of uncertain dynamical systems and show that this can be achieved by solving a non-classically constrained analytic interpolation problem. In particular, this non-classical constraint confines…
When methods of moments are used for identification of power spectral densities, a model is matched to estimated second order statistics such as, e.g., covariance estimates. If the estimates are good there is an infinite family of power…
We study the influence of analytical regularization used in the generalized function (distribution) space to the Tikhonov regularization procedure utilized in the different versions of Moore-Penrose's inversion. By introducing a new…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…