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arXiv · 2311.07035

ContHutch++: Stochastic trace estimation for implicit integral operators

Jennifer Zvonek·Andrew Horning·Alex Townsend
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Abstract

Hutchinson's estimator is a randomized algorithm that computes an $\epsilon$-approximation to the trace of any positive semidefinite matrix using $\mathcal{O}(1/\epsilon^2)$ matrix-vector products. An improvement of Hutchinson's estimator, known as Hutch++, only requires $\mathcal{O}(1/\epsilon)$ matrix-vector products. In this paper, we propose a generalization of Hutch++, which we call ContHutch++, that uses operator-function products to efficiently estimate the trace of any trace-class integral operator. Our ContHutch++ estimates avoid spectral artifacts introduced by discretization and are accompanied by rigorous high-probability error bounds. We use ContHutch++ to derive a new high-order accurate algorithm for quantum density-of-states and also show how it can estimate electromagnetic fields induced by incoherent sources.

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Jennifer Zvonek, Andrew Horning, Alex Townsend. 2023-11-13. ContHutch++: Stochastic trace estimation for implicit integral operators. https://arxiv.org/abs/2311.07035

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