Re: Looking for an algorithm: polynomial eigenvalue problem


<carlos@xxxxxxxxxxxx> wrote in message
news:1121447779.238191.20640@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> Have you tried a web search? Googling polynomial eigenproblems
> gives me 1510 hits, for example #3 is a nice presentation on
> linearization
>
> www.ma.man.ac.uk/~higham/talks/talk05_acme.pdf
>
> Some particular cases have been extensively studied because of
> important applications. E.g. N=2 appears in linearized flutter, also
> in linearized mechanical vibrations with nonproportional damping.
>
> Another name for that expression (by Peter Lancaster) is
> "lambda matrix" and he's got 2 books on the subject still
> in print, but do not deal with the computational side.


Thanks for the links and suggestions, Carlos.
Yes, I had done some web searches, but it wasn't until after my
original post that I ran across a clear discussion of the
linearization method -- the same paper by Mackey et al mentioned in
your link. Also, I ran across one of Lancaster's books yesterday,
and ordered it (very nice to find it as a Dover publication!)

At this point, I have coded a straightforward version of a basic
linearization
in Mathematica and it seems to work fine on randomly generated problems of
modest size.

Thanks again,
alan





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