Faster Stochastic Trace Estimation with a Chebyshev Product Identity

Eric Hallman

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arXiv · 2101.00325

Faster Stochastic Trace Estimation with a Chebyshev Product Identity

Eric Hallman

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Abstract

Methods for stochastic trace estimation often require the repeated evaluation of expressions of the form $z^T p_n(A)z$, where $A$ is a symmetric matrix and $p_n$ is a degree $n$ polynomial written in the standard or Chebyshev basis. We show how to evaluate these expressions using only $\lceil n/2\rceil$ matrix-vector products, thus substantially reducing the cost of existing trace estimation algorithms that use Chebyshev interpolation or Taylor series.

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Eric Hallman. 2021-01-01. Faster Stochastic Trace Estimation with a Chebyshev Product Identity. https://arxiv.org/abs/2101.00325

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