Timeline for Perturbation theory for $UV^*$ in singular value decomposition
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
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| Nov 30, 2021 at 3:16 | comment | added | user7868 | I know that $UV^*$ satisfies $UV^*=A(A^*A)^{-\frac{1}{2}}$ - it's the unitary part of the polar decomposition of $A$. I don't think it satisfies $UV^*=A|A|^{-1}$ if $|A|$ is the determinant. I could get a perturbation bound by in terms of the condition number of $A$ and a linear approximation for $A \mapsto (A^*A)^{-\frac{1}{2}}$, using the perturbation theory for $A\mathbf{x}=\mathbf{b}$, but I'd been hoping there'd be something better. | |
| Nov 30, 2021 at 2:16 | comment | added | Narutaka OZAWA | It's just about $UV^*=A|A|^{-1}$ ? | |
| Nov 30, 2021 at 1:09 | history | asked | user7868 | CC BY-SA 4.0 |