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Journal of Applied Mathematics
Volume 2013, Article ID 392034, 5 pages
http://dx.doi.org/10.1155/2013/392034
Research Article

A Subspace Embedding Method in Norm via Fast Cauchy Transform

The State Key Laboratory for High Performance Computation, National University of Defense and Technology, Changsha, Hunan 410073, China

Received 27 September 2013; Accepted 2 December 2013

Academic Editor: Hector Pomares

Copyright © 2013 Xu Xiang and Li-Zhi Cheng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We propose a subspace embedding method via Fast Cauchy Transform (FCT) in norm. It is motivated by and complements the work of the subspace embedding method in norm, for all except , by K. L. Clarkson (ACM-SIAM, 2013). Unlike the traditionally used orthogonal basis in Johnson-Lindenstrauss (JL) embedding, we employ the well-conditioned basis in norm to obtain concentration property of FCT in norm.