Talk:Generalized minimal residual method

message: I'm confused by the pseudocode. First, c and s are never initialized. Second, there seems to be no convergence criteria. So, is this to find the exact x after all n steps? If so, what good is it? JefeDeJefes 20:49, 17 January 2007 (UTC)
replies: text: I don't understand your first point. All entries in c and s are initialized before they are used (in the first iteration of the j-loop, the i-loop is skipped because the sequence 1, … j-1 is empty). Your second point is spot on: the algorithm finds the exact x after n steps, and no, this is not very useful. The algorithm needs to be amended and cleaned up. -- Jitse Niesen (talk) 14:50, 30 March 2007 (UTC)
thread_title:  Pseudocode 

message: The text states that the n-th Krylov subspace is defined as
: K_n = \operatorname{span} \, \{ b, Ab, A^2b, \ldots, A^{n-1}b \} \, 
where b is the right-hand side of the system we want to solve.
I think this should be substituted by
: K_n = \operatorname{span} \, \{ r, Ar, A^2r, \ldots, A^{n-1}r \} \, 
where  r is the initial residual.
Otherwise you could choose  b as one eigenvector and the initial iterate  x_0 as a different one and your Krylov subspace certainly never contains the solution vector.
Or did I misunderstand something?  —Preceding unsigned comment added by 195.176.179.209 (talk) 07:41, 23 December 2010 (UTC)
thread_title:  Wrong definition of Krylov subspaces? 

message: I was able to understand the entire page regarding Conjugate Gradient Method just fine.
But I'm not getting anything out of this page.
I heard about Krylov Subspace before, but I still don't know what it is and why it needs to be mentioned here.
Of course a set of not linear independent vectors creates a space
-- but why does this need to be mentioned here?!
And this is just one term on this page which is superfluous and potentially of interest to pure mathematicians (in contrary to applied mathematicians) only -- and they won't look on this page anyway.
Everywhere on this page new expressions are introduced without explaining what they stand for!
I think the first sentence on this page should mention what is being minimized by this method -- I was thinking |Ax-b|^2.  — Preceding unsigned comment added by 192.73.228.23 (talk) 22:19, 12 December 2012 (UTC)
replies: text: I absolutely agree. I'm just trying to get a little background info on this method so I understand how it's used to fit actual data, but I couldn't decipher all of the jargon in this page. Wikipedia is supposed to be for general public use, not for measuring manhoods and competing to see who can write the page so that the fewest possible people can understand it. --Zoharalson (talk) 20:39, 27 June 2013 (UTC)
replies: text: Krylov subspace is the correct technical term for a subspace generated by the repeated application of a matrix to a vector. It is quite usual to express the analysis of gradient and quasi-Newton methods in terms of Krylov subspaces. You will find this term quite often if you are going to explore the inner workings of those methods.--LutzL (talk) 18:04, 28 June 2013 (UTC)
thread_title:  intentional obfuscation -- somebody trying to show off with his knowledge of obscure math terms?! 

message: The english version states for symmetric positive matrices:
 \|r_n\| \leq \left( \frac{2\kappa_2(A)-1}{2\kappa_2(A)} \right)^{n/2} \|r_0\| 
whereas boh the german and japanese versions state
\|r_m\|_2 \leq \left(\frac{\kappa_2^2(A)-1}{\kappa_2^2(A)}\right)^{m/2} \|r_0\|_2.
Which one is correct?  — Preceding unsigned comment added by 193.54.112.22 (talk) 15:28, 7 June 2013 (UTC)
thread_title:  Error in convergence? 

message: I am familiar with the history of GMRES, but I have never heard DIIS mentioned.  Is there a published literature review that mentions this relation?  A quick reading of Pulay's 1980 paper shows he misses the Arnodli process and the underlying theory for the GMRES polynomial (although he gets tantalizing close).  As it stands, calling GMRES a special case of DIIS is like calling the Wright Flyer a special case of Langley's Aerodrome.
Jeffreyhokanson (talk) 16:13, 27 November 2013 (UTC)
thread_title:  History 

message: 192.73.228.23 (talk) 00:09, 6 February 2014 (UTC)
thread_title:  iterative process -- is n incremented somewhere? 

message: 192.73.228.23 (talk) 00:15, 6 February 2014 (UTC)
thread_title:  Why is this a Krylov subspace method as it is not using a polynomial of A? 

message: 192.73.228.23 (talk) 00:25, 6 February 2014 (UTC)
thread_title:  assuming that n indicates the nth step, is the dimension of the sub problem increasing by one at every step? 

message: A*Qn = Qn+1*Hn
but Qn+1 depends on xn+1 which we are trying to calculate right now...  — Preceding unsigned comment added by 192.73.228.23 (talk) 01:05, 6 February 2014 (UTC)
thread_title:  H<sub>n</sub> is a time machine...