Re: Complexity of 'eigs'

[Søren Hauberg]

On Aug 13, 2012, at 12:06 PM, c. wrote:

> 
> On 13 Aug 2012, at 12:01, Søren Hauberg wrote:
> 
>> Thanks, that helped quite a bit, actually. I am fine with having the 
>> complexity of each iteration, which I understood to be O(D^3) if the matrix 
>> is dense DxD.
> 
> If your matrix is dense I am not sure using "eigs" rather than "eig" is 
> convenient, the deirect algorithm in "eig" should be O(D^2):
> http://web.eecs.utk.edu/~dongarra/etemplates/node93.html#sec:dense

The way I read the text at this link, 'eig' is O(D^3), but perhaps I'm missing 
something. I understand this as, first the matrix is put into tridiagonal form, 
which is O(D^3), and then another method (i.e. QR) is applied to get the 
eigenvectors, which takes O(D^2). Am I misunderstanding something?

Practially, I actually find 'eigs' to be faster than 'eig' if I only care about 
the first eigenvector; if I want them all, then 'eig' is better.

Søren