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

Julien M. Hendrickx; Alex Olshevsky

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arXiv · 0908.1397

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

Julien M. Hendrickx·Alex Olshevsky

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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.

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Julien M. Hendrickx, Alex Olshevsky. 2009-08-10. Matrix P-norms are NP-hard to approximate if p \neq 1,2,\infty. https://arxiv.org/abs/0908.1397

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