Related papers: The fast reduced QMC matrix-vector product

Many large scale problems in computational fluid dynamics such as uncertainty quantification, Bayesian inversion, data assimilation and PDE constrained optimization are considered very challenging computationally as they require a large…

We show how to obtain a fast component-by-component construction algorithm for higher order polynomial lattice rules. Such rules are useful for multivariate quadrature of high-dimensional smooth functions over the unit cube as they achieve…

Recovering matrices from compressive and grossly corrupted observations is a fundamental problem in robust statistics, with rich applications in computer vision and machine learning. In theory, under certain conditions, this problem can be…

Quantum Monte Carlo (QMC) methods have received considerable attention over the last decades due to their great promise for providing a direct solution to the many-body Schrodinger equation in electronic systems. Thanks to their low scaling…

We present a randomized algorithm for producing a quasi-optimal hierarchically semi-separable (HSS) approximation to an $N\times N$ matrix $A$ using only matrix-vector products with $A$ and $A^T$. We prove that, using $O(k \log(N/k))$…

Product between mode-$n$ unfolding $\bY_{(n)}$ of an $N$-D tensor $\tY$ and Khatri-Rao products of $(N-1)$ factor matrices $\bA^{(m)}$, $m = 1,..., n-1, n+1, ..., N$ exists in algorithms for CANDECOMP/PARAFAC (CP). If $\tY$ is an error…

A cardinal obstacle to performing quantum-mechanical simulations of strongly-correlated matter is that, with the theoretical tools presently available, sufficiently-accurate computations are often too expensive to be ever feasible. Here we…

Quantum Monte Carlo (QMC) methods are often used to calculate properties of many body quantum systems. The main cost of many QMC methods, for example the variational Monte Carlo (VMC) method, is in constructing a sequence of Slater matrices…

Quantiles and expected shortfalls are usually used to measure risks of stochastic systems, which are often estimated by Monte Carlo methods. This paper focuses on the use of quasi-Monte Carlo (QMC) method, whose convergence rate is…

We study distributed low rank approximation in which the matrix to be approximated is only implicitly represented across the different servers. For example, each of $s$ servers may have an $n \times d$ matrix $A^t$, and we may be interested…

In this paper, we consider the problem of efficiently computing the eigenvalues of limited-memory quasi-Newton matrices that exhibit a compact formulation. In addition, we produce a compact formula for quasi-Newton matrices generated by any…

There have been several algorithms designed to optimise matrix multiplication. From schoolbook method with complexity $O(n^3)$ to advanced tensor-based tools with time complexity $O(n^{2.3728639})$ (lowest possible bound achieved), a lot of…

We analyze the convergence of higher order Quasi-Monte Carlo (QMC) quadratures of solution-functionals to countably-parametric, nonlinear operator equations with distributed uncertain parameters taking values in a separable Banach space $X$…

This article provides a survey of recent research efforts on the application of quasi-Monte Carlo (QMC) methods to elliptic partial differential equations (PDEs) with random diffusion coefficients. It considers, and contrasts, the uniform…

Efficiently approximating local curvature information of the loss function is a key tool for optimization and compression of deep neural networks. Yet, most existing methods to approximate second-order information have high computational or…

Many data analysis applications deal with large matrices and involve approximating the matrix using a small number of ``components.'' Typically, these components are linear combinations of the rows and columns of the matrix, and are thus…

Monte Carlo integration is a widely used numerical method for approximating integrals, which is often computationally expensive. In recent years, quantum computing has shown promise for speeding up Monte Carlo integration, and several…

Recently, Pagh presented a randomized approximation algorithm for the multiplication of real-valued matrices building upon work for detecting the most frequent items in data streams. We continue this line of research and present new {\em…

Monte Carlo (MC) integration has been employed as the standard approximation method for the Sliced Wasserstein (SW) distance, whose analytical expression involves an intractable expectation. However, MC integration is not optimal in terms…

Several studies have shown the ability of natural gradient descent to minimize the objective function more efficiently than ordinary gradient descent based methods. However, the bottleneck of this approach for training deep neural networks…