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Given $A,B\in\Bbb R^{n\times n}$ is there a technique find $\min_{ T\in O(n,\Bbb R)}\|A-TBT^{-1}\|_F$ or $\min_{ T\in O(n,\Bbb R)}\|A-TBT^{-1}\|_2$ in polynomial in $\log(\|A\|_2\|B\|_2),n,1/\epsilon$ time where $\epsilon>0$ is error from true value?

Given $A,B\in\Bbb R^{n\times n}$ is there technique find $$\min_{ T\in O(n,\Bbb R)}\|A-TBT^{-1}\|_F\mbox{ or }\min_{ T\in O(n,\Bbb R)}\|A-TBT^{-1}\|_2$$ within additive approximation error in $\epsilon>0$ in $O\big(\big(\frac{n\cdot\log(\|A\|_2\|B\|_2)}\epsilon\big)^c\big)$ time at fixed $c>0$?

Given $A,B\in\Bbb R^{n\times n}$ is there a technique find $\min_{ T\in O(n,\Bbb R)}\|A-TBT^{-1}\|_F$ or $\min_{ T\in O(n,\Bbb R)}\|A-TBT^{-1}\|_2$ at least for special cases of Hermitian or skew Hermitian?

Given $A,B\in\Bbb R^{n\times n}$ is there a technique find $\min_{ T\in O(n,\Bbb R)}\|A-TBT^{-1}\|_F$ or $\min_{ T\in O(n,\Bbb R)}\|A-TBT^{-1}\|_2$ in polynomial in $\log(\|A\|_2\|B\|_2),n,1/\epsilon$ time where $\epsilon>0$ is error from true value?

Given $A,B\in\Bbb R^{n\times n}$ is there a technique find $\min_{ T\in O(n,\Bbb R)}\|A-TBT^{-1}\|_F$ or $\min_{ T\in O(n,\Bbb R)}\|A-TBT^{-1}\|_2$?

Given $A,B\in\Bbb R^{n\times n}$ is there a technique find $\min_{ T\in O(n,\Bbb R)}\|A-TBT^{-1}\|_F$ or $\min_{ T\in O(n,\Bbb R)}\|A-TBT^{-1}\|_2$ at least for special cases of Hermitian or skew Hermitian?