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ugly Plot Eigenvalues ?

    Dear Mathematica friends,

How can I plot Re Eigenvalues as a function of a parameter
without unwanted ugly connections between branches?
In the example (computed by Mathematica 4.2 for HP-UX PA-RISC)

   m1={{8., 8, 7}, {0, 5, 5}, {8, 0, 0}}
   m2={{6., 0, 6}, {10, 8, 3}, {5, 8, 6}}
   Plot[Evaluate[Re[Eigenvalues[m1+w*m2]]], {w,-3,3}];

for w approximately -0.4 there is an unwanted vertical bar.
This is related to "ordering" of solutions to equation.

Is there a simple nice solution for this and related examples?
(taking exact numbers in the example above avoids the unwanted connection,
but this is not a good solution for a general machine precission problem)

Pavel Pokorny
Math Dept, Prague Institute of Chemical Technology

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