Oct
13
comment Grid engine and shared libraries
Hi choroba. Thanks for the answer. How do I know if there is a shared drive and how to locate it?
Oct
13
asked Grid engine and shared libraries
Oct
13
comment Grid engine cluster + OpenCV: strange behaviour
@Vince: Yes I have access to those nodes. Do I have to install the libraries to all of these nodes? Maybe I have just to modify the sge_conf file and change the SET_LIB_PATH variable? (linux.die.net/man/5/sge_conf)
Oct
11
awarded Yearling
Oct
11
awarded Yearling
Oct
10
asked Grid engine cluster + OpenCV: strange behaviour
Oct
10
awarded Commentator
Oct
10
comment How to include graphics from parent directory using \graphicspath?
Did you find a solution ? Thanks.
Oct
5
accepted How to compute the induced matrix norm $\| \cdot \|_{2,\infty}$
Oct
5
comment How to compute the induced matrix norm $\| \cdot \|_{2,\infty}$
Thanks. I had figured it out too: $\|A\|_{2,\infty}=\|A^T\|_{1,2}$.
Oct
4
awarded Scholar
Oct
4
accepted On the induced matrix norm $\| \cdot \|_{2,\infty}$
Oct
4
comment On the induced matrix norm $\| \cdot \|_{2,\infty}$
@NathanielJohnston: In that paper, $\| A \|_{p,q}$ denotes $\sup_{x\in\mathbb{R}^n\setminus \{0\}} \frac{\|Ax\|_q}{\|x\|_p}$, which is like the other, so it is probably mistaken. Thanks and +1. Suvrit: hmm, it seems that there is no conventional notation. I have seen some authors used $\|\cdot\|_{pq}$ or $\|\cdot\|_{p\to q}$ to denote the induced norm of the linear operator mapping $l_p\to l_q$, but haven't seen any thing like $\|\cdot\|_{qp}$ :P (In addition, some use $\|\cdot\|_{pq}$ or $|\cdot |_{pq}$ for the vector norm).
Oct
3
awarded Editor
Oct
3
revised On the induced matrix norm $\| \cdot \|_{2,\infty}$
Changed $mathbb{R}^n\to mathbb{R}^n$ to $mathbb{R}^n\to mathbb{R}^m$
Oct
3
comment On the induced matrix norm $\| \cdot \|_{2,\infty}$
But now I have another problem. The paper you cited (Paper 2) contradicts the paper that I cited (Paper 1). The equation (2h) in Paper 1 says that $\|A\|_{\infty,2}$ is the largest 2-norm of any row, while in Paper 2 this should be the value of $\|A\|_{2,\infty}$.
Oct
3
comment On the induced matrix norm $\| \cdot \|_{2,\infty}$
Thanks, Suvrit and @NathanielJohnston. I had figured it out too. The adjoint operator of $A$, mapping $(\mathbb R^m , \| \cdot \|_p^*) = (\mathbb R^m , \| \cdot \|_{p/(p-1)})$ to $(\mathbb R^n, \| \cdot \|_q^*) = (\mathbb R^n, \| \cdot \|_{p/(p-1)})$ is the transpose matrix $A^T$. Since $\|A\|_{p,q} = \|A^T\|_{q/(q-1),p/(p-1)}$, we have $\|A\|_{2,\infty}=\|A^T\|_{1,2}$ and so we can apply the result of the case $1\to 2$. (next below)
Oct
3
awarded Student
Oct
3
asked On the induced matrix norm $\| \cdot \|_{2,\infty}$
Oct
3
revised How to compute the induced matrix norm $\| \cdot \|_{2,\infty}$
added one more question
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