Papers › Randomized block-Krylov subspace methods for low-rank approximation of matrix functions
Randomized block-Krylov subspace methods for low-rank approximation of matrix functions
David Persson, Tyler Chen, Christopher Musco
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The randomized SVD is a method to compute an inexpensive, yet accurate, low-rank approximation of a matrix. The algorithm assumes access to the matrix through matrix-vector products (matvecs). Therefore, when we would like to apply the randomized SVD to a matrix function, f(A), one needs to approximate matvecs with f(A) using some other algorithm, which is typically treated as a black-box. Chen and Hallman (SIMAX 2023) argued that, in the common setting where matvecs with f(A) are approximated using Krylov subspace methods (KSMs), a more efficient low-rank approximation is possible if we open this black-box. They present an alternative approach that significantly outperforms the naive combination of KSMs with the randomized SVD, although the method lacked theoretical justification. In this work, we take a closer look at the method, and provide strong and intuitive error bounds that justify its excellent performance for low-rank approximation of matrix functions.
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