Related papers: Faster Linear Systems and Matrix Norm Approximatio…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…
In this paper, we present a simple combinatorial algorithm that solves symmetric diagonally dominant (SDD) linear systems in nearly-linear time. It uses very little of the machinery that previously appeared to be necessary for a such an…
A growing number of problems in computational mathematics can be reduced to the solution of many linear systems that are related, often depending smoothly or slowly on a parameter $p$, that is, $A(p)x(p)=b(p)$. We introduce an efficient…
We deal with interval parametric systems of linear equations and the goal is to solve such systems, which basically comes down to finding an enclosure for a parametric solution set. Obviously we want this enclosure to be as tight as…
Linear regression is a fundamental and primitive problem in supervised machine learning, with applications ranging from epidemiology to finance. In this work, we propose methods for speeding up distributed linear regression. We do so by…
Momentum Iterative Hessian Sketch (M-IHS) techniques, a group of solvers for large scale regularized linear Least Squares (LS) problems, are proposed and analyzed in detail. Proposed M-IHS techniques are obtained by incorporating the Heavy…
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…
This paper presents fast solvers for linear systems arising from the discretization of fractional nonlinear Schr\"odinger equations with Riesz derivatives and attractive nonlinearities. These systems are characterized by complex symmetry,…
We present the first near optimal approximation schemes for the maximum weighted (uncapacitated or capacitated) $b$--matching problems for non-bipartite graphs that run in time (near) linear in the number of edges. For any…
We show how to approximate a data matrix $\mathbf{A}$ with a much smaller sketch $\mathbf{\tilde A}$ that can be used to solve a general class of constrained k-rank approximation problems to within $(1+\epsilon)$ error. Importantly, this…
We present an asymptotically faster algorithm for solving linear systems in well-structured 3-dimensional truss stiffness matrices. These linear systems arise from linear elasticity problems, and can be viewed as extensions of graph…
We develop a fast solver for the spectral element method (SEM) applied to the two-sided fractional diffusion equation on uniform, geometric and graded meshes. By approximating the singular kernel with a degenerate kernel, we construct a…
This survey describes probabilistic algorithms for linear algebra computations, such as factorizing matrices and solving linear systems. It focuses on techniques that have a proven track record for real-world problem instances. The paper…
A linearly implicit conservative difference scheme is applied to discretize the attractive coupled nonlinear Schr\"odinger equations with fractional Laplacian. Complex symmetric linear systems can be obtained, and the system matrices are…
Sketch-and-solve (SAS) is a very successful method to efficiently estimate the solution of heavily overdetermined large linear least squares problems. It uses random sketching to reduce the size of the problem, hence reducing the…
This paper aims to accelerate the test-time computation of deep convolutional neural networks (CNNs). Unlike existing methods that are designed for approximating linear filters or linear responses, our method takes the nonlinear units into…
We propose a new globally convergent stochastic second order method. Our starting point is the development of a new Sketched Newton-Raphson (SNR) method for solving large scale nonlinear equations of the form $F(x)=0$ with $F:\mathbb{R}^p…
Iterative methods based on matrix splittings are useful in solving large sparse linear systems. In this direction, proper splittings and its several extensions are used to deal with singular and rectangular linear systems. In this article,…
We consider online statistical inference of constrained stochastic nonlinear optimization problems. We apply the Stochastic Sequential Quadratic Programming (StoSQP) method to solve these problems, which can be regarded as applying…