Re: eigenvalue calculation for asymmetric matrix with smooth profile



Robert Israel wrote:
"poriahd@xxxxxxxxx" <poriahd@xxxxxxxxx> writes:

On Sep 26, 1:19 pm, spellu...@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
(Peter Spellucci) wrote:
In article <1190790262.332375.63...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"pori...@xxxxxxxxx" <pori...@xxxxxxxxx> writes:

>On Sep 24, 7:48 pm, spellu...@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
>>(Peter Spellucci) wrote:

>> In article <1190641269.216891.282...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
>> "pori...@xxxxxxxxx" <pori...@xxxxxxxxx> writes:
>>
>> >Hi every body
......
>
>then you could solve the eigenvalue problem by any standard code for
>one alpha
>

what you describe simply means that your eigensolver doesn't sort the
eigenvalues itself, (which is quite common. the eigenvalues are not
necessarily found in some fixed order)
hence my remark: sorting the eigenvalues yourself should
be no problem.
but if there occur multiple eigenvalues , then a crossing in the
curves could occur. this can be smooth or unsmooth depending on the
special structure of the eigensystem occuring at that alpha. hence my
hint to use extrapolation along the piece of curve already determined
in order
to detect and deal properly with that. but as long as the eigenvalues
stay pairwise different, such trouble doesn't occur.

hth
peter
Dear peter

you said sorting the eigenvalues yourself should be no problem. Please
help me how can I sort eigenvalues? what algoritm exist for sorting
eigenvalue?

The same algorithms that you could use to sort any other list of items
(quicksort, bubble sort, heapsort, ...)

Except that complex numbers need a 2 index sort, for example modulus and then phase.

Dan
.

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