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MATRIX p-NORMS ARE NP-HARD TO APPROXIMATE IF p not equal to 1, 2, infinity

Author(s)
Hendrickx, Julien; Olshevsky, Alexander
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Abstract
We show that, for any rational p ∈ [1,∞) [p is an element of the set [1, infinity)] except p = 1, 2, unless P = NP, there is no polynomial time algorithm which approximates the matrix p-norm to arbitrary relative precision. We also show that, for any rational p ∈ [1,∞) [p is an element of the set [1, infinity)] including p = 1, 2, unless P = NP, there is no polynomialtime algorithm which approximates the ∞, p [infinity, p] mixed norm to some fixed relative precision.
Date issued
2010-10
URI
http://hdl.handle.net/1721.1/64956
Department
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Journal
SIAM Journal on Matrix Analysis and Applications
Publisher
Society for Industrial and Applied Mathematics
Citation
Hendrickx, Julien M., and Alex Olshevsky. “Matrix $p$-Norms Are NP-Hard to Approximate If $p\neq1,2,\infty$.” SIAM Journal on Matrix Analysis and Applications 31.5 (2010) : 2802. © 2010 Society for Industrial and Applied Mathematics
Version: Final published version
ISSN
0895-4798
1095-7162

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