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- W4287100438 abstract "In this work we obtain results related to the approximation of $h$-dimensional dominant subspaces and low rank approximations of matrices $ Ainmathbb K^{mtimes n}$ (where $mathbb K=mathbb R$ or $mathbb C)$ in case there is no singular gap at the index $h$, i.e. if $sigma_h=sigma_{h+1}$ (where $sigma_1geq ldotsgeq sigma_pgeq 0$ denote the singular values of $ A$, and $p=min{m,n}$). In order to do this, we develop a novel perspective for the convergence analysis of the classical deterministic block Krylov methods in this context. Indeed, starting with a matrix $ Xinmathbb K^{ntimes r}$ with $rgeq h$ satisfying a compatibility assumption with some $h$-dimensional right dominant subspace, we show that block Krylov methods produce arbitrarily good approximations for both problems mentioned above. Our approach is based on recent work by Drineas, Ipsen, Kontopoulou and Magdon-Ismail on approximation of structural left dominant subspaces. The main difference between our work and previous work on this topic is that instead of exploiting a singular gap at $h$ (which is zero in this case) we exploit the nearest existing singular gaps." @default.
- W4287100438 created "2022-07-25" @default.
- W4287100438 creator A5015755763 @default.
- W4287100438 date "2021-07-05" @default.
- W4287100438 modified "2023-09-30" @default.
- W4287100438 title "Dominant subspace and low-rank approximations from block Krylov subspaces without a gap" @default.
- W4287100438 doi "https://doi.org/10.48550/arxiv.2107.01990" @default.
- W4287100438 hasPublicationYear "2021" @default.
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