[1812.09042] Low-rank Approximation of Linear Maps
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Statistics > Machine Learning

arXiv:1812.09042 (stat)
[Submitted on 21 Dec 2018 (v1), last revised 6 Jan 2023 (this version, v2)]

Title:Low-rank Approximation of Linear Maps

Authors:Patrick Heas, Cedric Herzet
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Abstract:This work provides closed-form solutions and minimum achievable errors for a large class of low-rank approximation problems in Hilbert spaces. The proposed theorem generalizes to the case of bounded linear operators the previous results obtained in the finite dimensional case for the Frobenius norm. The theorem provides the basis for the design of tractable algorithms for kernel or continuous DMD.
Subjects: Machine Learning (stat.ML); Machine Learning (cs.LG)
Cite as: arXiv:1812.09042 [stat.ML]
  (or arXiv:1812.09042v2 [stat.ML] for this version)
  https://doi.org/10.48550/arXiv.1812.09042

Submission history

From: Patrick Heas [view email]
[v1] Fri, 21 Dec 2018 10:54:18 UTC (116 KB)
[v2] Fri, 6 Jan 2023 10:57:30 UTC (118 KB)
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