Timeline for The minimal norm of a shifted stochastic matrix
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 1, 2013 at 11:32 | comment | added | Daniel86 | @S. Sra , your comments lead me to think that it depends on how close $\sigma_{1}$ is to 1, see my edit above. What do you think? | |
| Mar 25, 2013 at 1:47 | comment | added | Suvrit | Try the Pascal matrix (for which the bounds should be derivable, or at least estimable analytically) --- (this matrix can be generated in Matlab using the command 'pascal'); for this matrix, it seems that $\|M-ee^T/n\|_2 > 0.5\sigma_1$, and that the gap between $\sigma_1$ and $\sigma_2$ is fairly large (of course, I scaled the matrix to be row-stochastic before testing the above claims) | |
| Mar 24, 2013 at 20:57 | comment | added | Daniel86 | Thank you for your insights. I also figured that $\alpha = 1$ yields the minimum value also for the spectral norm. However, can you think of a matrix with a large gap between $\sigma_{1}$ and $\sigma_{2}$ (let's say, depends on $n$) for which this expression is as large as a factor of $\sigma_{1}$? I have some (maybe wrong) intuition that it decreases with the second singular values (maybe depends on $n$). | |
| Mar 24, 2013 at 17:52 | history | edited | Suvrit | CC BY-SA 3.0 |
updated answer to include numerical example.
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| Mar 24, 2013 at 5:35 | history | answered | Suvrit | CC BY-SA 3.0 |