1. XTRACE: MAKING THE MOST OF EVERY SAMPLE IN STOCHASTIC TRACE ESTIMATION.
- Author
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EPPERLY, ETHAN N., TROPP, JOEL A., and WEBBER, ROBERT J.
- Subjects
- *
BUDGET , *ALGORITHMS - Abstract
The implicit trace estimation problem asks for an approximation of the trace of a square matrix, accessed via matrix-vector products (matvecs). This paper designs new randomized algorithms, XTrace and XNysTrace, for the trace estimation problem by exploiting both variance reduction and the exchangeability principle. For a fixed budget of matvecs, numerical experiments show that the new methods can achieve errors that are orders of magnitude smaller than existing algorithms, such as the Girard--Hutchinson estimator or the Hutch++ estimator. A theoretical analysis confirms the benefits by offering a precise description of the performance of these algorithms as a function of the spectrum of the input matrix. The paper also develops an exchangeable estimator, XDiag, for approximating the diagonal of a square matrix using matvecs. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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