Accelerating Matrix Trace Estimation by Aitken’s Δ2 Process

ICASSP 2023 - 2023 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)(2023)

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Abstract
We present an algorithm to estimate the trace of symmetric matrices that are available only via Matrix-Vector multiplication. The proposed algorithm constructs a series of trace estimates by applying the probing technique with an increasing number of vectors. These estimates are then treated as a converging sequence whose limit is the sought matrix trace, and we apply Aitken’s Δ 2 process to accelerate its convergence to the trace limit. Numerical experiments performed on covariance matrices demonstrate the competitiveness of the proposed scheme versus probing and randomized trace estimators.
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Key words
Aitken Δ2 process,algorithm constructs,converging sequence whose limit,matrix trace estimation,matrix-vector multiplication,probing technique,sought matrix trace,symmetric matrices,trace estimates,trace limit
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