Related papers: On the discrepancy principle
We consider the reconstruction of a diffusion coefficient in a quasilinear elliptic problem from a single measurement of overspecified Neumann and Dirichlet data. The uniqueness for this parameter identification problem has been established…
We further investigate the uniform regularity property of collections of sets via primal and dual characterizing constants. These constants play an important role in determining convergence rates of projection algorithms for solving…
We study the application of the Augmented Lagrangian Method to the solution of linear ill-posed problems. Previously, linear convergence rates with respect to the Bregman distance have been derived under the classical assumption of a…
We consider a rational system of first order difference equations in the plane with four parameters such that all fractions have a common denominator. We study, for the different values of the parameters, the global and local properties of…
The article addresses the convergence of implicit and semi-implicit, fully discrete approximations of a class of nonlinear parabolic evolution problems. Such schemes are popular in the numerical solution of evolutions defined with the…
Given a set of items and a set of evaluators who all individually rank them, how do we aggregate these evaluations into a single societal ranking? Work in social choice and statistics has produced many aggregation methods for this problem,…
Standard rational expectations models with an occasionally binding zero lower bound constraint either admit no solutions (incoherence) or multiple solutions (incompleteness). This paper shows that deviations from full-information rational…
The coefficient of variation is a useful indicator for comparing the spread of values between dataset with different units or widely different means. In this paper we address the problem of investigating the equality of the coefficients of…
The discrepancy function measures the deviation of the empirical distribution of a point set in $[0,1]^d$ from the uniform distribution. In this paper, we study the classical discrepancy function with respect to the BMO and exponential…
Variational regularization and the quasisolutions method are justified for unbounded closed, possibly nonlinear, operators. The argument is quite simple and yields general results.
In this article, we present a simpler and alternative proof of the solvability of the regularity problem - that is, the Dirichlet problem with boundary data in $\dot W^{1,p}$ - for uniformly elliptic operators on $\mathbb{R}^n_+$ under a…
We establish the large deviation principle for solutions of one-dimensional SDEs with discontinuous coefficients. The main statement is formulated in a form similar to the classical Wentzel--Freidlin theorem, but under the considerably…
In this paper we provide a convergence analysis of some variational methods alternative to the classical Tikhonov regularization, namely Ivanov regularization (also called method of quasi solutions) with some versions of the discrepancy…
We present some forms of uncertainty principle which involve in a new way localization operators, the concept of $\varepsilon$-concentration and the standard deviation of $L^2$ functions. We show how our results improve the classical…
We provide an asymptotic analysis of linear transport problems in the diffusion limit under minimal regularity assumptions on the domain, the coefficients, and the data. The weak form of the limit equation is derived and the convergence of…
In this paper we consider switched nonlinear systems under average dwell time switching signals, with an otherwise arbitrary compact index set and with additional constraints in the switchings. We present invariance principles for these…
Analytic number theorists usually seek to show that sequences which appear naturally in arithmetic are ``well-distributed'' in some appropriate sense. In various discrepancy problems, combinatorics researchers have analyzed limitations to…
In many iterative optimization methods, fixed-point theory enables the analysis of the convergence rate via the contraction factor associated with the linear approximation of the fixed-point operator. While this factor characterizes the…
Flexible sparsity regularization means stably approximating sparse solutions of operator equations by using coefficient-dependent penalizations. We propose and analyse a general nonconvex approach in this respect, from both theoretical and…
This Note derives regularity bounds for a Gevrey criterion when the Cauchy problem of elliptic equations is solved by regularization. When utilizing the regularization, one knows that checking such criterion is basically problematic, albeit…