English

Matrix P-norms are NP-hard to approximate if p \neq 1,2,\infty

Computational Complexity 2010-04-26 v3

Abstract

We show that for any rational p \in [1,\infty) except p = 1, 2, unless P = NP, there is no polynomial-time algorithm for approximating the matrix p-norm to arbitrary relative precision. We also show that for any rational p\in [1,\infty) including p = 1, 2, unless P = NP, there is no polynomial-time algorithm approximates the \infty, p mixed norm to some fixed relative precision.

Keywords

Cite

@article{arxiv.0908.1397,
  title  = {Matrix P-norms are NP-hard to approximate if p \neq 1,2,\infty},
  author = {Julien M. Hendrickx and Alex Olshevsky},
  journal= {arXiv preprint arXiv:0908.1397},
  year   = {2010}
}

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12 pages