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

[Helmut Jarausch <jarausch@xxxxxxxxxxxxxxxxxxx>]

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