Re: Matrix Minimax, sorta

Am 19.10.05 12:27 schrieb Hauke Reddmann:
> I have the equation aA+bB+cC+...=min.,
> where a,b,c... are scalars, A,B,C are matrices,
> a=b=c=...=0 is ruled out and "min." isn't
> Euclidean norm but the rank.
>
> For special cases (e.g. two 2x2 matrices - just
> fix a/b so that the determinant vanishes) this
> is easy, but can you give a general approach?
>
No real idea; but may be this could be an approach:
reformat all matrices to vectors,
A -> va (nxn -> 1*n²)
B -> vb (nxn -> 1*n²)
...
and then try a multiple regression of vb,vc,... on va.
This should at least give small differences between
the entries of A and the entries of a prediction
matrix constructed by b*B + c*C + ...

Perhaps the regression-method can be meaningful adapted
to optimize for zeroes of blocks of entries in the residual
"a*va" minus "predicted", which jointly define a whole column ...


But -as I said: I don't know whether this leads to anywhere...

Gottfried Helms


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