### Web: http://arxiv.org/abs/2202.05120

June 20, 2022, 1:11 a.m. | Ainesh Bakshi, Kenneth L. Clarkson, David P. Woodruff

We study iterative methods based on Krylov subspaces for low-rank
approximation under any Schatten-$p$ norm. Here, given access to a matrix $A$
through matrix-vector products, an accuracy parameter $\epsilon$, and a target
rank $k$, the goal is to find a rank-$k$ matrix $Z$ with orthonormal columns
such that $\| A(I -ZZ^\top)\|_{S_p} \leq (1+\epsilon)\min_{U^\top U = I_k} \|A(I - U U^\top)\|_{S_p}$, where $\|M\|_{S_p}$ denotes the $\ell_p$ norm of
the the singular values of $M$. For the special cases of $p=2$ (Frobenius …

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