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 <[email protected]> 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: > [email protected] > <https://outlook.office.com/mail/options/mail/[email protected]> > *|* Tel: +31(0)6 438 666 87 *|* > *|* Netherlands eScience Center <https://www.esciencecenter.nl/> *|* Science > Park 140 *|* 1098 XG Amsterdam *| *The Netherlands *|* > *| Twitter <https://twitter.com/eScienceCenter> | LinkedIn > <https://www.linkedin.com/company/netherlands-escience-center> | Facebook > <https://www.facebook.com/NLeScienceCenter/> | YouTube > <https://www.youtube.com/channel/UCYLAIMi62d8tx3Ru6DOSPeg> | Newsletter > <https://esciencecenter.us8.list-manage.com/subscribe/post?u=a0a563ca342f1949246a9f92f&id=31bfc2303d> > |* > > > > ------------------------------ > *From:* Peter <[email protected]> > *Sent:* Wednesday, January 20, 2021 19:19 > *To:* [email protected] <[email protected]> > *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 > > >
