This is an announcement for the paper "A variant of the Johnson-Lindenstrauss lemma for circulant matrices" by Jan Vybiral.
Abstract: We continue our study of the Johnson-Lindenstrauss lemma and its connection to circulant matrices started in \cite{HV}. We reduce the bound on $k$ from $k=O(\varepsilon^{-2}\log^3n)$ proven there to $k=O(\varepsilon^{-2}\log^2n)$. Our technique differs essentially from the one used in \cite{HV}. We employ the discrete Fourier transform and singular value decomposition to deal with the dependency caused by the circulant structure.
Archive classification: math.FA
Mathematics Subject Classification: 52C99, 68Q01
The source file(s), Johnson_Lind2.tex: 21785 bytes, is(are) stored in gzipped form as 1002.2847.gz with size 8kb. The corresponding postcript file has gzipped size 84kb.
Submitted from: jan.vybiral@oeaw.ac.at
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http://front.math.ucdavis.edu/1002.2847
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http://arXiv.org/abs/1002.2847
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