Krylov-aware stochastic trace estimation

Tyler Chen; Eric Hallman

doi:10.1137/22m1494257

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arXiv · 2205.01736

Krylov-aware stochastic trace estimation

Tyler Chen·Eric Hallman

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Abstract

We introduce an algorithm for estimating the trace of a matrix function $f(\mathbf{A})$ using implicit products with a symmetric matrix $\mathbf{A}$. Existing methods for implicit trace estimation of a matrix function tend to treat matrix-vector products with $f(\mathbf{A})$ as a black-box to be computed by a Krylov subspace method. Like other recent algorithms for implicit trace estimation, our approach is based on a combination of deflation and stochastic trace estimation. However, we take a closer look at how products with $f(\mathbf{A})$ are integrated into these approaches which enables several efficiencies not present in previously studied methods. In particular, we describe a Krylov subspace method for computing a low-rank approximation of a matrix function by a computationally efficient projection onto Krylov subspace.

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Tyler Chen, Eric Hallman. 2022-05-03. Krylov-aware stochastic trace estimation. https://doi.org/10.1137/22m1494257

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