Does anyone know the procedure (or have pseudo code) to approximating the largest eigenvalue of a monodromy matrix? Or even to approximate the monodromy matrix itself?
There is no explicit solution to acquire the fundamental matrix in this case.
If you can afford the CPU time and storage, compute the monodromy matrix explicitly by solving $n$ IVPs with the vectors of the canonical basis.
Otherwise, use Arnoldi, possibly in the default functions included in your computing environment (e.g., Matlab's eigs
, or scipy.sparse.linalg.eigs
), providing a callback function that evaluates f(v)=Av
by solving an IVP.
Afun
on it.mathworks.com/help/matlab/ref/…). If you have doubts with definitions and basic facts about monodromy matrices, I am afraid that Mathoverflow is not the right place to ask about it.
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Jun 18, 2016 at 17:41