Re: [eigen] finding dominant eigenvalue/vector : is Power Iteration the best method? |

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On 02/09/2012 05:36:20 PM, Mark Borgerding wrote:
> Does anyone know of a faster way of getting a decent (e.g. RMSE<1e-4)
> estimate of the single most dominant eigenvalue and a vector in its
> eigenspace?
>
> http://en.wikipedia.org/wiki/Power_iteration
>
> Other may converge with faster "big O" complexity per iteration
> (Inverse
> Iteration, Rayleigh quotient iteration) , but they often require
> inverting the matrix or solving a system per iteration, which seems
> to
>
> inflate the cost per iteration considerably compared to a simple
> matrix-by-vector multiply and normalization.
I'd use a block variant of the power method approximating several of
the largest eigenvalues. This helps a lot if there is no "big" gap
between the first and second eigenvalues.
Furthermore you may have a look at
http://www.staff.science.uu.nl/~sleij101/
Helmut.
--
Helmut Jarausch
Lehrstuhl fuer Numerische Mathematik
RWTH - Aachen University
D 52056 Aachen, Germany