Talk:Kaczmarz method

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Randomized version

Latest comment: 13 years ago2 comments2 people in discussion

The discussion on randomized version is still very academic (all references were published last year). There are many improvements over the Kaczmarz algorithm in the literature, most of which more widely accepted than this one. Should this part be deleted? —Preceding unsigned comment added by 141.132.89.81 (talk) 01:46, 29 January 2010 (UTC)Reply

No, I think the randomized method is now pretty much main stream and quite important. No reason not to be up to date.Billlion (talk) 08:55, 19 January 2012 (UTC)Reply

Disambig of Richard Gordon?

Latest comment: 6 years ago3 comments3 people in discussion

Hello - We currently have a link to Richard Gordon. Can someone more familiar with this topic verify that we want it to point to Richard Gordon (theoretical biologist)? Thanks KConWiki (talk) 13:22, 21 April 2013 (UTC)Reply

@KConWiki: Done on 7 April 2014 by Nick Number in Special:Diff/603203260. --CiaPan (talk) 08:39, 24 January 2019 (UTC)Reply
Better late than never... :-)

Ah, I remember it like it was yesterday. This doesn't speak well of my ability to remember what I did yesterday. Nick Number (talk) 17:04, 24 January 2019 (UTC)Reply

Eq 1 what is bi?

Latest comment: 6 years ago2 comments2 people in discussion

Term is undefined. — Preceding unsigned comment added by 149.142.201.252 (talk) 18:30, 6 June 2018 (UTC)Reply

This is quite standard notation for an element of a vector. Specifically, ${\displaystyle b_{i}}$  is an i-th component (item, coordinate) of the ${\displaystyle B}$  vector. --CiaPan (talk) 19:53, 25 January 2019 (UTC)Reply

Eq 1 what is <a,x> notation?

Latest comment: 4 years ago1 comment1 person in discussion

Propose to add the definition of what the brackets mean, just like the symbol for complex conjugate is defined. — Preceding unsigned comment added by 2A02:2149:8610:6D00:71C5:E9:4439:66A0 (talk) 22:51, 15 February 2021 (UTC)Reply

Inconsistent norm notation in proof

Latest comment: 4 months ago1 comment1 person in discussion

In the proof of Algorithm 2, the matrix norm is defined as

${\displaystyle \|A\|^{2}=\sum _{j=1}^{m}\|a_{j}\|^{2}}$ 

Meaning it's the Frobenius Norm.

However, elsewhere in the proof, ${\displaystyle \|A^{-1}\|}$  is used as the least singular value, meaning the norm is the Spectral Norm. This is pretty confusing.

In the actual paper, they say this:

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The usual condition number of \(A\) is

${\displaystyle k(A):=\|A\|_{2}\,\|A^{-1}\|_{2}.}$ 

A related version is the scaled condition number introduced by Demmel:

${\displaystyle \kappa (A):=\|A\|_{F}\,\|A^{-1}\|_{2}.}$ 

One easily checks that

${\displaystyle 1\;\leq \;{\frac {\kappa (A)}{\sqrt {n}}}\;\leq \;k(A).}$ 

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The proof in the article should probably be updated to distinguish the ${\displaystyle \|_{F}}$  norm from the ${\displaystyle \|_{2}}$  norm; and also warn about the use of "condition number" is different from its standard definition. Thomasda (talk) 08:23, 10 April 2025 (UTC)Reply