MATRIX p-NORMS ARE NP-HARD TO APPROXIMATE IF p ≠ 1, 2, ∞

被引：71
|
作者：
Hendrickx, Julien M. [1 ]
Olshevsky, Alex [1 ]
机构：
[1] MIT, Informat & Decis Syst Lab, Cambridge, MA 02139 USA
来源：
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2010年 / 31卷 / 05期
基金：
美国国家科学基金会;
关键词：
matrix norms; complexity; NP-hardness;
D O I：
10.1137/09076773X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show that, for any rational p is an element of [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 is an element of [1, infinity) including p = 1, 2, unless P = NP, there is no polynomial-time algorithm which approximates the infinity, p mixed norm to some fixed relative precision.
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页码：2802 / 2812
页数：11
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