Re: Looking for an algorithm: polynomial eigenvalue problem

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.

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