Timeline for How to solve a quadratic matrix equation with positive semidefinite constraint?
Current License: CC BY-SA 4.0
7 events
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| Jul 20, 2020 at 17:36 | history | edited | Rodrigo de Azevedo | CC BY-SA 4.0 |
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| Nov 9, 2019 at 8:02 | answer | added | Federico Poloni | timeline score: 3 | |
| Nov 7, 2019 at 10:09 | comment | added | Markus Sprecher | Let $f(X)=XAX+X$ we have $f(X+dX)=f(X)+dX\cdot A\cdot X+X\cdot A\cdot dX+dX+O(|dX|^2)$. We could define an iteration by $X_{k+1}=X_k+dX$ where $dX$ is the solution to $f(X_k)+dX\cdot A\cdot X_k+X_k\cdot A\cdot dX+dX=B$. This is a continuous Lyapunov equation. | |
| Nov 7, 2019 at 10:04 | comment | added | Markus Sprecher | another iteration would be $X_{k+1}=B-X_k A X_k$. This would preserve the symmetry of the matrix and, if you start close enough to a solution, also the positive definiteness. If it converges depends however on $A$ and $B$. | |
| Nov 7, 2019 at 8:14 | history | edited | lisi | CC BY-SA 4.0 |
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| Nov 7, 2019 at 8:09 | history | edited | lisi | CC BY-SA 4.0 |
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| Nov 7, 2019 at 7:55 | history | asked | lisi | CC BY-SA 4.0 |