Related papers: Discretization of a matrix in the problem of quadr…
Matrices are exceptionally useful in various fields of study as they provide a convenient framework to organize and manipulate data in a structured manner. However, modern matrices can involve billions of elements, making their storage and…
This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the…
Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel finite element discretization that results in exponential convergence at pre-selected points. The two key…
When factorizing binary matrices, we often have to make a choice between using expensive combinatorial methods that retain the discrete nature of the data and using continuous methods that can be more efficient but destroy the discrete…
Neural networks have recently been employed as material discretizations within adjoint optimization frameworks for inverse problems and topology optimization. While advantageous regularization effects and better optima have been found for…
This paper is concerned with algorithms and applications of decreasing minimization on an M-convex set, which is the set of integral elements of an integral base-polyhedron. Based on a recent characterization of decreasingly minimal…
Identifying informative components in binary data is an essential task in many research areas, including life sciences, social sciences, and recommendation systems. Boolean matrix factorization (BMF) is a family of methods that performs…
In this paper, a new iterative two-level algorithm is presented for solving the finite element discretization for nonsymmetric or indefinite elliptic problems. The iterative two-level algorithm uses the same coarse space as the traditional…
We present an amelioration of current known algorithms for optimal spectral partitioning problems. The idea is to use the advantage of a representation using density functions while decreasing the computational time. This is done by…
We consider the problem of discretizing one-dimensional, real-valued functions as graphs. The goal is to find a small set of points, from which we can approximate the remaining function values. The method for approximating the unknown…
Many problems of interest for cyber-physical network systems can be formulated as Mixed-Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithmic framework to solve…
Geometric particle-in-cell discretizations have been derived based on a discretization of the fields that is conforming with the de Rham structure of the Maxwell's equation and a standard particle-in-cell ansatz for the fields by deriving…
Matrices arising in scientific applications frequently admit linear low-rank approximations due to smoothness in the physical and/or temporal domain of the problem. In large-scale problems, computing an optimal low-rank approximation can be…
The data input model is a fundamental component of every quantum algorithm, as its efficiency is crucial for achieving potential speed-ups over classical methods. For quantum linear algebra tasks that utilize quantum eigenvalue or singular…
In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multiscale algorithms are designed to represent the fine-scale…
The domain of an optimization problem is seen as one of its most important characteristics. In particular, the distinction between continuous and discrete optimization is rather impactful. Based on this, the optimizing algorithm, analyzing…
We present an ordinary differential equations approach to the analysis of algorithms for constructing $l_1$ minimizing solutions to underdetermined linear systems of full rank. It involves a relaxed minimization problem whose minimum is…
Max-norm regularizer has been extensively studied in the last decade as it promotes an effective low-rank estimation for the underlying data. However, such max-norm regularized problems are typically formulated and solved in a batch manner,…
We discuss computational and qualitative aspects of the fractional Plateau and the prescribed fractional mean curvature problems on bounded domains subject to exterior data being a subgraph. We recast these problems in terms of energy…
In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In…