Timeline for Robust generalization of matrix rank
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 7, 2017 at 15:41 | comment | added | J.J. Green | There is a readable overview in Rank-Deficient and Discrete Ill-Posed Problems by Per Christian Hansen (1997) | |
| Apr 7, 2017 at 13:13 | answer | added | Vahan | timeline score: 0 | |
| Jan 8, 2016 at 13:04 | comment | added | MKR | Thanks to @SebastianGoette and other commentors for their usefull pointers. Searching for 'stable rank' I have found these useful lecture notes, which make precise the role of the singular value decomposition and the connection to stable rank. | |
| Jan 7, 2016 at 17:39 | comment | added | Sebastian Goette | @Suvrit The paper looks good, But my search engine produced things like Stable ranks of subalgebras of the ball algebras instead, which have nothing to do with this problem. Apparently, different communities have their own stable ranks. | |
| Jan 7, 2016 at 15:53 | comment | added | Suvrit | @SebastianGoette so in particular you don't think e.g., users.cms.caltech.edu/~jtropp/conf/Tro09-Column-Subset-SODA.pdf (see column 2) is fitting? Afaik, this quantity is now in "common" use. It does not exactly cover the OP, but may be interesting (esp. because it does not require picking a threshold below which all the singular values can be ignored). | |
| Jan 7, 2016 at 14:20 | comment | added | Federico Poloni | Other pointers to the literature are "numerical rank" or "$\varepsilon$-rank" (trickier to search for, because Google doesn't understand LaTeX). What you will find there is essentially the suggestion of Sebastian Goette: compute singular values, and treat small singular values as zeros. How large "small" can be is very application-specific; a rule of thumb is that if a singular value is smaller than the expected noise level then it should be treated as a zero (or a potential zero). | |
| Jan 7, 2016 at 14:02 | answer | added | Carlo Beenakker | timeline score: 1 | |
| Jan 7, 2016 at 13:28 | comment | added | Suvrit | search for "stable rank"... | |
| Jan 7, 2016 at 13:28 | comment | added | Sebastian Goette | If a matrix $A$ is close to one of low rank, then I would guess that some of its singular values (eigenvalues of $A^*A$) are very small, albeit nonzero. So you could look for a spectral gap for $A^*A$ and consider only eigenvalues above that. | |
| Jan 7, 2016 at 13:22 | history | asked | MKR | CC BY-SA 3.0 |