Talk:Krylov subspace

QMR?

I saw "QMR" mentioned in a README. It appears to be related to Krylov methods. Could someone explain what they are? —The preceding unsigned comment was added by BenFrantzDale (talk • contribs).

Could you provide a little more context? A "readme" file from where? QMR in relation to what? Lunch 23:13, 19 December 2006 (UTC)[reply]

It was in a readme for [1]. I think I found a link for QMR: [2], which suggests it's "Quasi-Minimal Residual". It looks like the best place for that sort of information right now would be on GMRES. (There was no "Minimal residual method"; I redirected that at GMRES for now; I'm not sure if it should have its own page.) —Ben FrantzDale 23:56, 19 December 2006 (UTC)[reply]

CG, BiCG(STAB), GMRES, MINRES, ORTHOMIN, and GBIT are all different algorithms. I'm not sure MINRES and ORTHOMIN see much use anymore. I think "Krylov solvers" would be a better redirect since GMRES isn't the same thing.

BTW, Yousuf Saad's "Iterative methods" book is a good reference. (There's a second edition that came out recently.)

Cheers, Lunch 18:50, 20 December 2006 (UTC)[reply]

I second that remark. I am currently reading Saad's book. It is very informative for a non-mathematician and provides the context for many aspects of optimization. Didactik (talk) 22:25, 21 August 2011 (UTC)[reply]

readability?

Hi, this article is currently unreadable for a person (like me) who is not an expert in numerical methods. I believe it would be a good idea to start with a description of Krylov's method, and then pass to generalisations and variations. Thanks, Sasha 4/3/2007

I'm not sure what you're expecting from the article. Could you explain what it is you'd like to see in the article? And, btw, there isn't the Krylov method but only a class of Krylov methods.

You are, of course, welcome to edit the article and expand it. It is just a stub (and is already marked as so). Lunch 01:59, 5 March 2007 (UTC)[reply]

PS The "Krylov subspace methods" section in iterative methods is even less readable; in fact, I did not understand a word. It would be great if someone would write a simple description of the original method of finding the eigenvalues iof a matrix. Sodin 01:34, 4 March 2007 (UTC)[reply]

If you're looking for a basic description of how to compute eigenvalues, you might want to check the eigenvalue article. Lunch 01:59, 5 March 2007 (UTC)[reply]

Hi, sorry, this was not meant to be personal. Now to business: As far as I rememeber, Krylov suggested his method as a numerically simple way to compute the eigenvalues of a matrix A (without computing the characteristic pol-l). He started from a vector v, and computed the minimal polynomial of v with less arithmetic computations (than needed to compute the char. pol-l). I thought this would appear in one of the articles starting with "Krylov", but alas... Unfortunately I do not remember neither the details nor the motivation well enough to write it myself. Best, Sodin 22:31, 5 March 2007 (UTC)[reply]