Re: Complexity of 'eigs'

[Søren Hauberg]

On Aug 13, 2012, at 12:25 PM, c. wrote:

> 
> On 13 Aug 2012, at 12:13, Søren Hauberg wrote:
> 
>> 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?
> 
> No, you're right mine was just a typo. 

Ok.

>> 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.
> 
> I would not expect the advantage of "eigs" over "eig" to be very important if 
> your matrix is dense and you do not need to compute the eigenvectors.
> But maybe I am missing some implementation detail.

I need the actual eigenvectors (not just the eigenvalues). Does that make a 
difference?

Søren