Related papers: Sparsified Cholesky and Multigrid Solvers for Conn…
Multiscale modeling is a systematic approach to describe the behavior of complex systems by coupling models from different scales. The approach has been demonstrated to be very effective in areas of science as diverse as materials science,…
We address the problem of finding the nearest graph Laplacian to a given matrix, with the distance measured using the Frobenius norm. Specifically, for the directed graph Laplacian, we propose two novel algorithms by reformulating the…
Rearranging the rows or columns of a sparse matrix using an appropriate ordering can significantly reduce fill-ins, i.e., new nonzeros introduced during matrix factorization, decreasing memory usage and runtime. However, finding an ordering…
Graph matching is a challenging problem with very important applications in a wide range of fields, from image and video analysis to biological and biomedical problems. We propose a robust graph matching algorithm inspired in…
Boundary detection has long been a fundamental tool for image processing and computer vision, supporting the analysis of static and time-varying data. In this work, we built upon the theory of Graph Signal Processing to propose a novel…
Square matrices appear in many machine learning problems and models. Optimization over a large square matrix is expensive in memory and in time. Therefore an economic approximation is needed. Conventional approximation approaches factorize…
We consider approximating solutions to parameterized linear systems of the form $A(\mu_1,\mu_2) x(\mu_1,\mu_2) = b$. Here the matrix $A(\mu_1,\mu_2) \in \mathbb{R}^{n \times n}$ is nonsingular, large, and sparse and depends nonlinearly on…
Sparse recovery is widely applied in many fields, since many signals or vectors can be sparsely represented under some frames or dictionaries. Most of fast algorithms at present are based on solving $l^0$ or $l^1$ minimization problems and…
Graph sparsification is an area of interest in computer science and applied mathematics. Sparsification of a graph, in general, aims to reduce the number of edges in the network while preserving specific properties of the graph, like cuts…
For a linear matrix function $f$ in $X \in \R^{m\times n}$ we consider inhomogeneous linear matrix equations $f(X) = E$ for $E \neq 0$ that have or do not have solutions. For such systems we compute optimal norm constrained solutions…
The multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared to…
Tensor decomposition has emerged as a prominent technique to learn low-dimensional representation under the supervision of reconstruction error, primarily benefiting data inference tasks like completion and imputation, but not…
The essence of distantly supervised relation extraction is that it is an incomplete multi-label classification problem with sparse and noisy features. To tackle the sparsity and noise challenges, we propose solving the classification…
We introduce a method for sparsifying distributed algorithms and exhibit how it leads to improvements that go past known barriers in two algorithmic settings of large-scale graph processing: Massively Parallel Computation (MPC), and Local…
Estimating large covariance matrices has been a longstanding important problem in many applications and has attracted increased attention over several decades. This paper deals with two methods based on pre-existing works to impose sparsity…
Numerical algorithms have two kinds of costs: arithmetic and communication, by which we mean either moving data between levels of a memory hierarchy (in the sequential case) or over a network connecting processors (in the parallel case).…
In many problems in Computational Physics and Chemistry, one finds a special kind of sparse matrices, termed "banded matrices". These matrices, which are defined as having non-zero entries only within a given distance from the main…
We consider a sparse grid collocation method in conjunction with a time discretization of the differential equations for computing expectations of functionals of solutions to differential equations perturbed by time-dependent white noise.…
The sparse group Lasso is a widely used statistical model which encourages the sparsity both on a group and within the group level. In this paper, we develop an efficient augmented Lagrangian method for large-scale non-overlapping sparse…
We consider Gaussian Random Fields on metric graphs defined implicitly as the stationary solution to a fractional SPDE driven by Gaussian white noise. Sampling from the finite element approximation requires the Cholesky factorization of the…