Related papers: Fast and forward stable randomized algorithms for …
Data sketches are approximate succinct summaries of long streams. They are widely used for processing massive amounts of data and answering statistical queries about it in real-time. Existing libraries producing sketches are very fast, but…
We consider the problem of finding a sparse solution for an underdetermined linear system of equations when the known parameters on both sides of the system are subject to perturbation. This problem is particularly relevant to…
This paper derives a new variational equation for the linear least-squares backward error by expressing the backward error in terms of a generalized eigenvalue problem and using results from indefinite linear algebra. For problems with…
We present a novel distributed computing framework that is robust to slow compute nodes, and is capable of both approximate and exact computation of linear operations. The proposed mechanism integrates the concepts of randomized sketching…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
We present a sparse matrix permutation from graph theory that gives stable incomplete Lower-Upper (LU) preconditioners necessary for iterative solutions to the steady state density matrix for quantum optomechanical systems. This reordering…
We study the robustness of accelerated first-order algorithms to stochastic uncertainties in gradient evaluation. Specifically, for unconstrained, smooth, strongly convex optimization problems, we examine the mean-squared error in the…
We present a parallel algorithm for the undirected $s,t$-mincut problem with floating-point valued weights. Our overarching algorithm uses an iteratively reweighted least squares framework. This generates a sequence of Laplacian linear…
We develop a robust and efficient iterative method for hyper-elastodynamics based on a novel continuum formulation recently developed. The numerical scheme is constructed based on the variational multiscale formulation and the…
Many challenging tasks in sensor networks, including sensor calibration, ranking of nodes, monitoring, event region detection, collaborative filtering, collaborative signal processing, {\em etc.}, can be formulated as a problem of solving a…
In regularized risk minimization, the associated optimization problem becomes particularly difficult when both the loss and regularizer are nonsmooth. Existing approaches either have slow or unclear convergence properties, are restricted to…
This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the…
This article proposes and analyzes several variants of the randomized Cholesky QR factorization of a matrix $X$. Instead of computing the R factor from $X^T X$, as is done by standard methods, we obtain it from a small, efficiently…
We conduct a study and comparison of superiorization and optimization approaches for the reconstruction problem of superiorized/regularized least-squares solutions of underdetermined linear equations with nonnegativity variable bounds.…
Linear stability of inviscid, parallel, and stably stratified shear flow is studied under the assumption of smooth strictly monotonic profiles of shear flow and density, so that the local Richardson number is positive everywhere. The…
We propose a randomized algorithm with quadratic convergence rate for convex optimization problems with a self-concordant, composite, strongly convex objective function. Our method is based on performing an approximate Newton step using a…
Among randomized numerical linear algebra strategies, so-called sketching procedures are emerging as effective reduction means to accelerate the computation of Krylov subspace methods for, e.g., the solution of linear systems, eigenvalue…
We present a new algorithm for solving linear-quadratic regulator (LQR) problems with linear equality constraints, also known as constrained LQR (CLQR) problems. Our method's sequential runtime is linear in the number of stages and…
This work is a continuation of "Fast and backward stable computation of roots of polynomials" by J.L. Aurentz, T. Mach, R. Vandebril, and D.S. Watkins, SIAM Journal on Matrix Analysis and Applications, 36(3): 942--973, 2015. In that paper…
Bayesian modelling and computational inference by Markov chain Monte Carlo (MCMC) is a principled framework for large-scale uncertainty quantification, though is limited in practice by computational cost when implemented in the simplest…