Timeline for How to solve a matrix equation with both inverses and a hadamard product?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Aug 25, 2016 at 17:07 | comment | added | Federico Poloni | @DaeyoungLim It's possible that there is one, but I don't know of any result that applies to that case. Matrix equations with Hadamard products are not very commonly studied, as far as I know. | |
| Aug 25, 2016 at 16:56 | comment | added | Daeyoung | @FedericoPoloni Is there any chance there is a closed form solution for this equation if $B$ and $C$ are both symmetric? I've encountered an equation of the same form and am stuck at the moment... | |
| Oct 19, 2013 at 0:44 | comment | added | Mike Izbicki | I've tried hammering my equation into a form suitable for your method, but unfortunately I don't think I can get it there. I did manage to remove the Hadamard product though, so I've asked another question here: mathoverflow.net/questions/145225/… . | |
| Oct 16, 2013 at 21:33 | comment | added | Federico Poloni | If you are fine with any solution, a simple experiment could be running a fixed point iteration such as $X_{k+1}=(B+X_k\circ C)^{-1}$ (or Newton's method, if you want to be more sophisticated) and see if it leads you somewhere. | |
| Oct 16, 2013 at 21:31 | comment | added | Federico Poloni | Then probably the theory there doesn't apply to your case. The constraint that $A$ is SPD looks unusual -- typically in matrix eqns when one looks for symmetric solutions the equation itself has some "natural" symmetry, but this is not your case. | |
| Oct 16, 2013 at 19:39 | comment | added | Mike Izbicki | I require that $A$ be positive semidefinite. I have a vague hope that this is enough to make the solution unique, but if not I suspect that any solution would be equally useful for my application (a metric learning algorithm). I glanced through the paper you link. It's not obvious to me how to rewrite this equation into a suitable form, and I don't think my $B$ and $C$ obey any elementwise positive constraints. | |
| Oct 16, 2013 at 6:56 | history | answered | Federico Poloni | CC BY-SA 3.0 |