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Re: How to solve real valued system of quadratic equations


From: Juan Pablo Carbajal
Subject: Re: How to solve real valued system of quadratic equations
Date: Wed, 22 Mar 2017 23:04:25 +0100

On Wed, Mar 22, 2017 at 9:11 AM, mmuetzel <address@hidden> wrote:
> Hi,
>
> I am having problems solving the following system of l quadratic equations:
> a_i * M_ik,l * a_k = B_l
>
> All M_ik,l and B_l have real (non-complex) values. M_ik,l is symmetric in
> all l equations (M_ik,l = M_ki,l).
> I am interested in real valued a_i that solve that system of quadratic
> equations in a least-squares sense (l_max > i_max). l_max and i_max are both
> of magnitude 100 (give or take).
>
> The only idea that I theoretically came up with is to "simultaneously"
> diagonalize M_ik,l for all l:
> a_i * U_ij * S_jm,l * U_km * a_k = B_l
>
> And than solve for b_j = U_ij * a_i. But I do not know how to find U_ij
> (which must be real valued as well, I guess).
>
> Is there some variant of svd that diagonalizes several matrices in the same
> basis (in a least-squares sense)?
> Is there another way of solving that problem?
>
> Thanks already for any hints.
>
> Markus
>
> PS: Enjoy OctConf to everyone who is there.
>
>
>
> --
> View this message in context: 
> http://octave.1599824.n4.nabble.com/How-to-solve-real-valued-system-of-quadratic-equations-tp4682513.html
> Sent from the Octave - General mailing list archive at Nabble.com.
>
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Hi,

Nothing pops up in ind mind besides diagonalization to solve the
problem. In your case you want simultaneous diagonalization (related
to the generalized eingenvalue problem), although I do not know how
feasible it is with more than 2 matrices.

Cheers



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