Re: [eigen] lowest eigen value only

[Rasmus Munk Larsen <rmlarsen@xxxxxxxxxx>]

Indeed, but unless you have a good preconditioner (as I alluded to) or fast inverse, an iterative method will still have to "chew" its way through the entire spectrum. You'll save memory perhaps, but not time.

On Wed, Jan 20, 2021 at 11:19 AM Jens Wehner <J.Wehner@xxxxxxxxxxxxxxxxx> wrote:

Hey Peter,

if your system is reasonably large iterative methods could be what you are looking for

Libraries like https://github.com/yixuan/spectra implement such things on top of Eigen.

Cheers Jens

| Jens Wehner, PhD | eScience Research Engineer | Email: j.wehner@xxxxxxxxxxxxxxxxx | Tel: +31(0)6 438 666 87 |

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From: Peter <list@xxxxxxxxxxxxxxxxx>
Sent: Wednesday, January 20, 2021 19:19
To: eigen@xxxxxxxxxxxxxxxxxxx <eigen@xxxxxxxxxxxxxxxxxxx>
Subject: Re: [eigen] lowest eigen value only

 

Dear Rasmus,


Am 20.01.21 um 19:02 schrieb Rasmus Munk Larsen:

> I don't believe that functionality is currently available in Eigen.. In general, there is no terribly efficient algorithm for doing so, unless you have a cheap way to compute or apply the inverse of the original matrix. I am
> personally working on a fast implementation of ?stebz (spectral bisection) for Eigen, which along with tridiagonalization will make such functionality available and reasonably efficient. I hope to be able to submit a merge
> request within the next month or so. Of course, Dhillon & Parlett's "Holy Grail" algorithm behind DSYEVR might be better still, but I don't have any immediate plans of implementing it.

Thanks for your response, sounds interesting and I'd be interested in testing it.
Speed is not everything, I'm already be happy to save a little bit of memory.

All the best,
Peter