       Re: Help with minimization of Eigenvalues

• To: mathgroup at smc.vnet.net
• Subject: [mg87761] Re: Help with minimization of Eigenvalues
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Wed, 16 Apr 2008 07:14:11 -0400 (EDT)
• Organization: Uni Leipzig
• References: <fu4ll6\$sfq\$1@smc.vnet.net>

```Hi,

Eig[a_?NumericQ, b_?NumericQ] := With[{m = {{a, b}, {b, -a + 1}},
s = {{1, 0}, {0, 3 a}}},
Eigenvalues[N[{m, s}]] // First
]

may help.

Regards
Jens

Chimico wrote:
> Hi,
>
> I am trying to minimize a particular eigenvalue of a generalized
> eigenvalue problem that depends on a few parameters. I have the
> following problem:
>
> Suppose we have two matrices s and m like these (the real matrices are
> much more complicated)
>
> m = {{a, b}, {b, -a + 1}}
>
> s = {{1, 0}, {0, 3a}}
>
> If I define the function Eig
>
> Eig[a_, b_] := Eigenvalues[{m, s}]//First
>
> And use it with the FindMinimum function it does not work.
> Infact just calling
>
> Eig[1,2] gives the error
>
> Eigenvalues::gfargs:
>    Generalized Eigenvalues
>      arguments accept only matrices with machine real
>       and complex elements. More...
>
> Even inserting Evaluate[] into the Eigenvalues function does not work.
> What am I doing wrong?
> Any help would be appreciated :-)
> thanks  Dario
>
>

```

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