Talk:Lanczos algorithm

message: [] - an unfocused variety of Lanczos algorithm
—Preceding unsigned comment added by 134.219.166.104 (talk • contribs) 21:23, 1 September 2005
This doesn't have much but it does have a reference to a book mathworld on Lanczos Algorithm]—Preceding unsigned comment added by RJFJR (talk • contribs) 23:36, 25 September 2005
I don't believe this is the Lanczos algorithm at all.
It is the power method.
—Preceding unsigned comment added by 130.126.55.123 (talk • contribs) 01:04, 5 August 2006
I don't know if the algorithm is correct, but it's certainly different than the power method, and presented pretty clearly.  I think it's gotten me on the right track at least... Thanks. --Jjdonald (talk) 22:22, 17 December 2007 (UTC)
replies: text: It is not easy to say it's wrong or correct, since quite some information is missing in order to apply it: (a) how to choose v[1], (b) how to choose m, (c) how to recognize the eigenvalues of A among those of T_mm. Unfortunately, this vagueness is by no means eliminated by the Numerical stability section. — MFH:Talk 21:57, 12 September 2008 (UTC)
replies: text: It is certainly not completely correct: there's at least something faulty with the indices. — MFH:Talk 19:59, 8 December 2011 (UTC)

text: There is a paper about Non-Symmetric Lanczos' algorithm (compared to Arnoldi) by Jane Cullum. — MFH:Talk 20:07, 8 December 2011 (UTC)
thread_title:  Old comments that did not have a section of their own 

message: I really think that this sentense has nothing to do in the first paragraph! Please someone who understand anything about it should create a separate section and explain what this is about!
Alain Michaud (talk) 16:52, 19 February 2010 (UTC)
thread_title:  In Latent Semantic Indexing, for... 

message: I suppose that Peter Montgomery`s 1995 paper was very good, but I do not see the need to inform everyone about its existence. This topic is much too advanced to be discussed at the top of the page. Please move this (second paragraph) towards the end of the page.   
Alain Michaud (talk) 16:50, 19 February 2010 (UTC)
thread_title:  Block Lanczos algorithm 

message: It would be nice if variables are defined before (or just after) being used. For example, at the begining, U and \sigma_i are not defined and its confusing for non-expert public.
Felipebm (talk) 13:34, 17 May 2011 (UTC)
thread_title:  Define variables 

message: In the section "Power method for finding eigenvalues", the matrix A is represented as A=U\text{diag}(\sigma_i)U', which is true only for normal matrices. For the general case, SVD decomposition should be used, i.e. A=U\text{diag}(\sigma_i)V' where U and V are some orthogonal matrices.  — Preceding unsigned comment added by 89.139.52.157 (talk) 12:14, 24 April 2016 (UTC)
replies: text: It's not stated explicitly at that point, but presumably A is already taken to be Hermitian (as it needs to be for the Lanczos algorithm to work), which means it has an eigendecomposition of the form stated. Instead using the SVD decomposition in this argument won't work, because the entire point is that U' U = I so that the product telescopes! Possibly it would be clearer to just use A = U \operatorname{diag}(\sigma_i) U^{-1}, i.e., hold off on requiring orthogonality — the reason being that the paragraph in question is about the plain power method, which applies in a greater generality. 130.243.68.202 (talk) 13:01, 2 May 2017 (UTC)
thread_title:  problematic matrix decomposition 

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thread_title:  External links modified