Related papers: Spatially inhomogeneous linear inverse problems wi…

We consider linear inverse problems in a nonparametric statistical framework. Both the signal and the operator are unknown and subject to error measurements. We establish minimax rates of convergence under squared error loss when the…

Building up on classical linear formulations, we posit that a broad class of problems in signal synthesis and in signal recovery are reducible to the basic task of finding a point in a closed convex subset of a Hilbert space that satisfies…

The subject of this work is a new stochastic Galerkin method for second-order elliptic partial differential equations with random diffusion coefficients. It combines operator compression in the stochastic variables with tree-based spline…

A classical problem in elasticity theory involves an inhomogeneity embedded in a material of given stress and shear moduli. The inhomogeneity is a region of arbitrary shape whose stress and shear moduli differ from those of the surrounding…

In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…

This paper derives identification, estimation, and inference results using spatial differencing in sample selection models with unobserved heterogeneity. We show that under the assumption of smooth changes across space of the unobserved…

This paper considers the development of spatially adaptive smoothing splines for the estimation of a regression function with non-homogeneous smoothness across the domain. Two challenging issues that arise in this context are the evaluation…

We consider an adaptive algorithm for finite element methods for the isogeometric analysis (IGAFEM) of elliptic (possibly non-symmetric) second-order partial differential equations. We employ analysis-suitable T-splines of arbitrary odd…

This paper presents a general description of a parameter estimation inverse problem for systems governed by nonlinear differential equations. The inverse problem is presented using optimal control tools with state constraints, where the…

This paper is based on Tseng's exgradient algorithm for solving variational inequality problems in real Hilbert spaces. Under the assumptions that the cost operator is quasimonotone and Lipschitz continuous, we establish the strong…

This paper proposes a new method for estimating sparse precision matrices in the high dimensional setting. It has been popular to study fast computation and adaptive procedures for this problem. We propose a novel approach, called Sparse…

In this paper, we consider the spatially inhomogeneous diffusively driven inelastic Boltzmann equation in different cases: the restitution coefficient can be constant or can depend on the impact velocity (which is a more physically relevant…

In this paper, we address a manifold constrained nonsmooth optimization problem involving the composition of a weakly convex function and a smooth mapping under the availability of a parametrization of the manifold. To find a stationary…

For the spatially homogeneous Boltzmann equation with hard po- tentials and Grad's cutoff (e.g. hard spheres), we give quantitative estimates of exponential convergence to equilibrium, and we show that the rate of exponential decay is…

A new numerical method to solve an inverse source problem for the Helmholtz equation in inhomogenous media is proposed. This method reduces the original inverse problem to a boundary value problem for a coupled system of elliptic PDEs, in…

A theory of superefficiency and adaptation is developed under flexible performance measures which give a multiresolution view of risk and bridge the gap between pointwise and global estimation. This theory provides a useful benchmark for…

We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling. This poroelasticity problem suffers from rapidly oscillating material parameters, which calls for a thorough…

We propose a general analytical framework for single-facility continuous location problems under spatial demand uncertainty. In contrast to classical formulations based on discrete or regionally aggregated demands, the proposed model…

The problem of imaging of a moving target is formulated as a Coefficient Inverse Problem for a hyperbolic equation with its coefficient depending on all three spatial variables and time. As the initial condition, the point source running…

The discretization of least-squares problems for linear ill-posed operator equations in Hilbert spaces is considered. The main subject of this article concerns conditions for convergence of the associated discretized minimum-norm…