Related papers: Discretization of a matrix in the problem of quadr…
In this paper, we present a new approach to linearizing zero-one quadratic minimization problem which has many applications in computer science and communications. Our algorithm is based on the observation that the quadratic term of…
Quantum computing provides a powerful framework for tackling computational problems that are classically intractable. The goal of this paper is to explore the use of quantum computers for solving relevant problems in systems and control…
In the present work, we investigate the computational efficiency afforded by higher-order finite-element discretization of the saddle-point formulation of orbital-free density functional theory. We first investigate the robustness of viable…
Many real-world applications are addressed through a linear least-squares problem formulation, whose solution is calculated by means of an iterative approach. A huge amount of studies has been carried out in the optimization field to…
Kernel quadrature is widely used to approximate integrals of smooth functions, with worst-case error typically decaying at the minimax rate $n^{-\alpha/d}$ for smoothness $\alpha$ in dimension $d$. Existing rate-optimal methods often depend…
Given a parametrized family of finite frames, we consider the optimization problem of finding the member of this family whose coefficient space most closely contains a given data vector. This nonlinear least squares problem arises naturally…
We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices. A salient feature of the proposed factorization scheme is it decouples the…
This paper, broadly speaking, covers the use of randomness in two main areas: low-rank approximation and kernel methods. Low-rank approximation is very important in numerical linear algebra. Many applications depend on matrix decomposition…
We review basic design principles underpinning the construction of mimetic finite difference and a few finite volume and finite element schemes for mixed formulations of elliptic problems. For a class of low-order mixed-hybrid schemes, we…
Matrix representations are a powerful tool for designing efficient algorithms for combinatorial optimization problems such as matching, and linear matroid intersection and parity. In this paper, we initiate the study of matrix…
Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…
Matrices resulting from the discretization of a kernel function, e.g., in the context of integral equations or sampling probability distributions, can frequently be approximated by interpolation. In order to improve the efficiency, a…
To ensure the discrete maximum principle or solution positivity in finite volume schemes, diffusive flux is sometimes discretized as a conical combination of finite differences. Such a combination may be impossible to construct along…
When numerical solution of elliptic and parabolic partial differential equations is required to be highly accurate in space, the discrete problem usually takes the form of large-scale and sparse linear systems. In this work, as an…
We propose an effective and flexible way to assemble finite element stiffness and mass matrices in MATLAB. We apply this for problems discretized by edge finite elements. Typical edge finite elements are Raviart-Thomas elements used in…
There are existing standard solvers for tackling discrete optimization problems. However, in practice, it is uncommon to apply them directly to the large input space typical of this class of problems. Rather, the input is preprocessed to…
We propose a convex variational principle to find sparse representation of low-lying eigenspace of symmetric matrices. In the context of electronic structure calculation, this corresponds to a sparse density matrix minimization algorithm…
As soon as abstract mathematical computations were adapted to computation on digital computers, the problem of efficient representation, manipulation, and communication of the numerical values in those computations arose. Strongly related…
We prove new necessary and sufficient conditions to carry out a compact linearization approach for a general class of binary quadratic problems subject to assignment constraints as it has been proposed by Liberti in 2007. The new conditions…
This is a study of certain finite element methods designed for convection-dominated, time-dependent partial differential equations. Specifically, we analyze high order space-time tensor product finite element discretizations, used in a…