Related papers: The Optimal Gradient Estimates for Perfect Conduct…
In this paper, Cimmino's classical reflection algorithm for solving the $n\times n$ nonsingular linear system $A\bx=\bb$ is analysed through the lens of spectral theory. Reformulating the weighted iteration as…
An exact solution for electromagnetic wave diffraction at the junction of two-dimensional electron systems (2DES) is obtained and analyzed for electric field polarized along the edge. A special emphasis is paid to the metal-contacted and…
We study dynamics near the threshold for blowup in the focusing nonlinear Klein-Gordon equation $u_{tt}-u_{xx} + u - |u|^{2\alpha} u =0$ on the line. Using mixed numerical and analytical methods we find that solutions starting from even…
This paper considers the problem of unconstrained minimization of smooth convex functions having Lipschitz continuous gradients with known Lipschitz constant. We recently proposed an optimized gradient method (OGM) for this problem and…
In the context of electromagnetic absorption, it is obvious that for an infinite planar periodic structure illuminated by a plane wave, the maximum attainable absorptance, i.e., perfect absorption, is theoretically limited to 100% of the…
The proximal gradient algorithm has been popularly used for convex optimization. Recently, it has also been extended for nonconvex problems, and the current state-of-the-art is the nonmonotone accelerated proximal gradient algorithm.…
Finite-sum optimization plays an important role in the area of machine learning, and hence has triggered a surge of interest in recent years. To address this optimization problem, various randomized incremental gradient methods have been…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
We consider the symmetric FEM-BEM coupling that connects two linear elliptic second order partial differential equations posed in a bounded domain $\Omega$ and its complement, where the exterior problem is restated by an integral equation…
We study best-policy identification for finite-horizon risk-sensitive reinforcement learning under the entropic risk measure. Recent work established a constant gap in the exponential horizon dependence between lower and upper bounds on the…
We derive the normal and anomalous proper polarization functions and the screened Coulomb interactions in a two-dimensional superfluid electron-hole bilayer, including all first-order corrections beyond the Random Phase Approximation (RPA).…
In this paper, we study a priori error estimates for the finite element approximation of the nonlinear Schr\"{o}dinger-Poisson model. The electron density is defined by an infinite series over all eigenvalues of the Hamiltonian operator. To…
We consider the inverse problem of recovering an isotropic electrical conductivity from interior knowledge of the magnitude of one current density field generated by applying current on a set of electrodes. The required interior data can be…
The least gradient problem (minimizing the total variation with given boundary data) is equivalent, in the plane, to the Beckmann minimal-flow problem with source and target measures located on the boundary of the domain, which is in turn…
We develop a statistically robust framework for reconstructing metal--semiconductor contact regions using topological gradients. The inverse problem is formulated as the identification of an unknown contact region from boundary measurements…
Consider a 2D composites with non-overlapping equal inclusions imbedded in a host material of the normalized unit conductivity. The conductivity of inclusions takes two values $\sigma_1$ and $\sigma_2$ with the probabilities $p$ and $1-p$,…
The superior performance of ensemble methods with infinite models are well known. Most of these methods are based on optimization problems in infinite-dimensional spaces with some regularization, for instance, boosting methods and convex…
Replacing positivity constraints by an entropy barrier is popular to approximate solutions of linear programs. In the special case of the optimal transport problem, this technique dates back to the early work of Schr\"odinger. This approach…
The numerical analysis of elastic wave propagation in unbounded media may be difficult to handle due to spurious waves reflected at the model artificial boundaries. Several sophisticated techniques such as nonreflecting boundary conditions,…
Tunneling and Coulomb drag are sensitive probes of spontaneous interlayer phase coherence in bilayer two-dimensional electron systems at total Landau level filling factor $\nu_T = 1$. We find that the phase boundary between the interlayer…