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)
 * It was in a readme for . I think I found a link for QMR:, 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)
 * 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)
 * 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)

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)

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)


 * 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)

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)