448 citations · 1.8k across the 37 of their papers we have counts for
8 papers · 1 filter
Krylov-aware stochastic trace estimation
Tyler Chen, Eric Hallman
We introduce an algorithm for estimating the trace of a matrix function using implicit products with a symmetric matrix . Existing methods for implicit…
Precision-aware Deterministic and Probabilistic Error Bounds for Floating Point Summation
Eric Hallman, Ilse C. F. Ipsen
We analyze the forward error in the floating point summation of real numbers, for computations in low precision or extreme-scale problem dimensions that push the limits of the prec…
Monte Carlo Methods for Estimating the Diagonal of a Real Symmetric Matrix
Eric Hallman, Ilse C. F. Ipsen, Arvind Saibaba
For real symmetric matrices that are accessible only through matrix vector products, we present Monte Carlo estimators for computing the diagonal elements. Our probabilistic bounds…
Randomized algorithms for rounding in the Tensor-Train format
Hussam Al Daas, Grey Ballard, Paul Cazeaux +5
The Tensor-Train (TT) format is a highly compact low-rank representation for high-dimensional tensors. TT is particularly useful when representing approximations to the solutions o…
A Refined Probabilistic Error Bound for Sums
Eric Hallman
This paper considers a probabilistic model for floating-point computation in which the roundoff errors are represented by bounded random variables with mean zero. Using this model,…
A Multilevel Approach to Stochastic Trace Estimation
Eric Hallman, Devon Troester
This article presents a randomized matrix-free method for approximating the trace of , where is a large symmetric matrix and is a function analytic in a c…