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This work aims to enhance the guarantees for approximate matrix multiplication using stable rank.

July 8, 2015Open Access

Optimal approximate matrix product in terms of stable rank

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Randomized trial demonstrates improved guarantees for approximate matrix multiplication in matrices.

This work aims to enhance the guarantees for approximate matrix multiplication using stable rank.
Utilized a black box approach with subspace embedding guarantees.
Focused on dimensionality-reducing maps with $m = O(\tilde{r}/\varepsilon^2)$ rows.
Applied findings across various sketching matrices including randomized and sparse embeddings.
Achieved improved bounds compared to previous studies [MZ11, KVZ14].
Provided new quantitative enhancements for approximate least squares regression.
Improved dimensionality reduction guarantees for $k$-means clustering.

Cohen et al. (2015) studied this question.

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