MATRIX p-NORMS ARE NP-HARD TO APPROXIMATE IF p not equal to 1, 2, infinity
Name
Hendrickx-2010-MATRIX p-NORMS ARE NP-HARD TO APPROXIMATE IF p not equal 1, 2, infinity.pdf
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193.34 KB
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Author(s)
Hendrickx, Julien
Olshevsky, Alexander
Date Issued
October 2010
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
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.
MIT Department
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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DOI of Published Version
https://doi.org/10.1137/09076773x
