Related papers: Random sketching of operators with application to …

This paper aims to address two issues of integral equations for the scattering of time-harmonic electromagnetic waves by a perfect electric conductor with Lipschitz continuous boundary: ill-conditioned {boundary element Galerkin matrices}…

Sketching is a probabilistic data compression technique that has been largely developed in the computer science community. Numerical operations on big datasets can be intolerably slow; sketching algorithms address this issue by generating a…

Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…

Sketching is widely used in randomized linear algebra for low-rank matrix approximation, column subset selection, and many other problems, and it has gained significant traction in machine learning applications. However, sketching large…

We show that the expected solution operator of prototypical linear elliptic partial differential operators with random coefficients is well approximated by a computable sparse matrix. This result is based on a random localized orthogonal…

Two widely used randomized algorithms are the sketch-and-solve method for least-squares regression and the randomized SVD for low-rank approximation. These algorithms apply a random embedding to compress a target matrix, and they perform…

In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…

Parameter reduction has been an important topic in deep learning due to the ever-increasing size of deep neural network models and the need to train and run them on resource limited machines. Despite many efforts in this area, there were no…

Randomized algorithms, such as randomized sketching or stochastic optimization, are a promising approach to ease the computational burden in analyzing large datasets. However, randomized algorithms also produce non-deterministic outputs,…

We consider the problem of embedding a subset of $\mathbb{R}^n$ into a low-dimensional Hamming cube in an almost isometric way. We construct a simple, data-oblivious, and computationally efficient map that achieves this task with high…

Sampling of signals belonging to a low-dimensional subspace has well-documented merits for dimensionality reduction, limited memory storage, and online processing of streaming network data. When the subspace is known, these signals can be…

Koopman operators provide tractable means of learning linear approximations of non-linear dynamics. Many approaches have been proposed to find these operators, typically based upon approximations using an a-priori fixed class of models.…

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…

Operator learning, the approximation of mappings between infinite-dimensional function spaces using machine learning, has gained increasing research attention in recent years. Approximate operators, learned from data, can serve as efficient…

This article is concerned with the question of constructing effcient multigrid preconditioners for the linear systems arising when applying semismooth Newton methods to large-scale linear-quadratic optimization problems constrained by…

We study a preconditioner for a Hermitian positive definite linear system, which is obtained as the solution of a matrix nearness problem based on the Bregman log determinant divergence. The preconditioner is of the form of a Hermitian…

This paper argues that randomized linear sketching is a natural tool for on-the-fly compression of data matrices that arise from large-scale scientific simulations and data collection. The technical contribution consists in a new algorithm…

We present and analyze an algorithm designed for addressing vector-valued regression problems involving possibly infinite-dimensional input and output spaces. The algorithm is a randomized adaptation of reduced rank regression, a technique…

We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…

Sketching is one of the most fundamental tools in large-scale machine learning. It enables runtime and memory saving via randomly compressing the original large problem into lower dimensions. In this paper, we propose a novel sketching…