Timeline for Singular values of $X$ in $AX+XA=C$?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Sep 15, 2019 at 6:35 | comment | added | Federico Poloni | @YaroslavBulatov That's not surprising, because essentially with that method (since $A$ is symmetric) you are computing an SVD of the Kronecker product $I\otimes A + A^T \otimes I$, and then skipping the divisions by 0 gives you the minimum-norm solution, by the usual least squares theory. | |
| Sep 14, 2019 at 23:49 | comment | added | Yaroslav Bulatov | BTW, Matlab's fast eigenvector based lyap2.m is giving me same result as explicit least squares (had to modify it to skip dividing by 0 eigenvalues) -- github.com/msubhransu/matrix-sqrt/blob/master/lyap2.m (evals wolframcloud.com/obj/yaroslavvb/newton/lyapunov.nb) | |
| Sep 13, 2019 at 17:22 | vote | accept | Yaroslav Bulatov | ||
| Sep 12, 2019 at 18:17 | comment | added | Federico Poloni | @YaroslavBulatov Not that I know of. The only thing that comes to mind is that you can use LSQR (a large sparse least-squares algorithm) on the Kronecker form implicitly via its matvec operator. But I doubt that it's going to be competitive; the storage needed seem still quite high. | |
| Sep 12, 2019 at 18:05 | comment | added | Yaroslav Bulatov | Thanks for the reference! Is there a standard approach to get the least-squares solution to the Lyapunov equation? (besides using kronecker expansion -> least squares which is expensive) | |
| Sep 12, 2019 at 6:43 | history | answered | Federico Poloni | CC BY-SA 4.0 |