MATRIX p-NORMS ARE NP-HARD TO APPROXIMATE IF p not equal to 1, 2, infinity
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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
2010-10Department
Massachusetts Institute of Technology. Laboratory for Information and Decision SystemsJournal
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