Related papers: An O(N) Direct Solver for Integral Equations on th…
We propose the numerical methods for solution of the weakly regular linear and nonlinear evolutionary (Volterra) integral equation of the first kind. The kernels of such equations have jump discontinuities along the continuous curves…
Analyzing the worst-case performance of deep neural networks against input perturbations amounts to solving a large-scale non-convex optimization problem, for which several past works have proposed convex relaxations as a promising…
Many applications involve solving several boundary value problems on geometries that are local perturbations of an original geometry. The boundary integral equation for a problem on a locally perturbed geometry can be expressed as a low…
To improve the computational efficiencies of the real-space orbital-free density functional theory, this work develops a new single-grid solver by directly providing the closed-form solution to the inner iteration and using an improved…
The Riemann problem for first-order hyperbolic systems of partial differential equations is of fundamental importance for both theoretical and numerical purposes. Many approximate solvers have been developed for such systems; exact solution…
The numerical solution of dynamical systems with memory requires the efficient evaluation of Volterra integral operators in an evolutionary manner. After appropriate discretisation, the basic problem can be represented as a matrix-vector…
We propose an extremely versatile approach to address a large family of matrix nearness problems, possibly with additional linear constraints. Our method is based on splitting a matrix nearness problem into two nested optimization problems,…
We develop a multiresolution approach to the problem of polygonal curve approximation. We show theoretically and experimentally that, if the simplification algorithm A used between any two successive levels of resolution satisfies some…
Many problems in nonlinear analysis and optimization, among them variational inequalities and minimization of convex functions, can be reduced to finding zeros (namely, roots) of set-valued operators. Hence numerous algorithms have been…
This work addresses models (e.g. potential models of directed orbital systems- the manganates) in which an effective reduction dimensionality occurs as a result of a new symmetry which is intermediate between that of global and local gauge…
Typical areas of application of explicit dynamics are impact, crash test, and most importantly, wave propagation simulations. Due to the numerically highly demanding nature of these problems, efficient automatic mesh generators and…
We give a stochastic optimization algorithm that solves a dense $n\times n$ real-valued linear system $Ax=b$, returning $\tilde x$ such that $\|A\tilde x-b\|\leq \epsilon\|b\|$ in time: $$\tilde O((n^2+nk^{\omega-1})\log1/\epsilon),$$ where…
In this paper, a new methodology is proposed that allows for the low-complexity development of neural network (NN) based equalizers for the mitigation of impairments in high-speed coherent optical transmission systems. In this work, we…
We study first-order optimization methods obtained by discretizing ordinary differential equations (ODEs) corresponding to Nesterov's accelerated gradient methods (NAGs) and Polyak's heavy-ball method. We consider three discretization…
We develop several efficient algorithms for the classical \emph{Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input $n\times n$ matrix $A$, this…
Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical…
$\renewcommand{\Re}{\mathbb{R}}$ We develop a general randomized technique for solving "implic it" linear programming problems, where the collection of constraints are defined implicitly by an underlying ground set of elements. In many…
In this work, we develop a fully implicit Hybrid High-Order algorithm for the Cahn-Hilliard problem in mixed form. The space discretization hinges on local reconstruction operators from hybrid polynomial unknowns at elements and faces. The…
We present enhancements to the computational efficiency of exact exchange calculations using the density matrix and local support functions. We introduce a numerical method which avoids the explicit calculation the four-center two-electron…
This paper presents a fast high-order method for the solution of two-dimensional problems of scattering by penetrable inhomogeneous media, with application to high-frequency configurations containing (possibly) discontinuous refractivities.…