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• W3134871005 abstract "We relate the problem of best low-rank approximation in the spectral norm for a matrix $A$ to Kolmogorov $n$-widths and corresponding optimal spaces. We characterize all the optimal spaces for the image of the Euclidean unit ball under $A$ and we show that any orthonormal basis in an $n$-dimensional optimal space generates a best rank-$n$ approximation to $A$. We also present a simple and explicit construction to obtain a sequence of optimal $n$-dimensional spaces once an initial optimal space is known. This results in a variety of solutions to the best low-rank approximation problem and provides alternatives to the truncated singular value decomposition. This variety can be exploited to obtain best low-rank approximations with problem-oriented properties." @default.
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• W3134871005 date "2021-01-01" @default.
• W3134871005 modified "2023-10-16" @default.
• W3134871005 title "Best Low-rank Approximations and Kolmogorov $n$-widths" @default.
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• W3134871005 doi "https://doi.org/10.1137/20m1355720" @default.
• W3134871005 hasPublicationYear "2021" @default.
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