Timeline for Reference request: continuity of Cholesky factor
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 26, 2020 at 8:51 | comment | added | Federico Poloni | What is P_n in your reply in chat? Symmetric matrices? Then I guess your map is $A \mapsto A^T A$, not $A \mapsto A^2$. | |
| May 26, 2020 at 8:45 | comment | added | ABIM | Let us continue this discussion in chat. | |
| May 26, 2020 at 8:38 | comment | added | Federico Poloni | How do you plan to use this inverse? That is not clear to me. What is "this space"? | |
| May 26, 2020 at 8:34 | vote | accept | ABIM | ||
| May 25, 2020 at 12:36 | comment | added | Federico Poloni | I am not sure if one can come up with a deterministic criterion for $\Pi$ that solves this problem. For instance, if $A_{2n} = diag(1,1/n,0)$, $A_{2n+1}=diag(1,0,1/n)$, then it seems that one needs to choose the identity permutation on even indices and (23) on odd indices. So the sequence $A_{n}$ converges to the matrix $A$ in my answer, but $\Pi$ is not eventually constant. (The factors $R_n$ converge to $R$, though, so maybe there is a way out.) I don't have a ready answer, sorry. | |
| May 25, 2020 at 12:15 | comment | added | ABIM | But are there reasonable known criteria on a decomposition, or choice of $\Pi$ as a function of $A$, making the map $A\to \mbox{ Cholesky factor of A}$ continuous? For example with the requirement that $\|A -R\|_F$ be minimal be such a requirement? (I've never had this type of issue before, so I hope my question is not too misguided). | |
| May 25, 2020 at 11:57 | comment | added | Federico Poloni | It's up to you to define which decomposition exactly you need! | |
| May 25, 2020 at 11:44 | comment | added | ABIM | How can it be resolved? | |
| May 25, 2020 at 11:42 | vote | accept | ABIM | ||
| May 25, 2020 at 11:42 | |||||
| May 25, 2020 at 10:32 | history | answered | Federico Poloni | CC BY-SA 4.0 |