Talk:Lanczos algorithm: Difference between revisions

Revision as of 03:09, 11 September 2008

Revision as of 21:57, 12 September 2008

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[[http://en.wikipedia.org/wiki/Lanczos_algorithm]] - an unfocused variety of Lanczos algorithm

<span class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:134.219.166.104|134.219.166.104]] ([[User talk:134.219.166.104|talk]] • [[Special:Contributions/134.219.166.104|contribs]]) 21:23, 1 September 2005</span><!-- Template:Unsigned -->

This doesn't have much but it does have a reference to a book [http://mathworld.wolfram.com/LanczosAlgorithm.html mathworld on Lanczos Algorithm]]<span class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:RJFJR|RJFJR]] ([[User talk:RJFJR|talk]] • [[Special:Contributions/RJFJR|contribs]]) 23:36, 25 September 2005</span><!-- Template:Unsigned -->

I don't believe this is the Lanczos algorithm at all.

It is the power method.

<span class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:130.126.55.123|130.126.55.123]] ([[User talk:130.126.55.123|talk]] • [[Special:Contributions/130.126.55.123|contribs]]) 01:04, 5 August 2006</span><!-- Template:Unsigned -->

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. --[[User:Jjdonald|Jjdonald]] ([[User talk:Jjdonald|talk]]) 22:22, 17 December 2007 (UTC)

: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 chose ''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. &mdash; [[User:MFH|MFH]]:[[User talk:MFH|Talk]] 21:57, 12 September 2008 (UTC)

== Extracting information from tridiagonal matrix ==

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So Lanczos gives you a tridiagonal matrix. I think a link would be helpful which explains how to extract low eigenvalues/eigenvectors from this matrix. <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/209.6.144.249|209.6.144.249]] ([[User talk:209.6.144.249|talk]]) 06:30, 2 March 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->

:agreeAgree - or largest eigenvalues: anyway, the article starts by saying that it's for calculating eigenvalues, but then onlystops describeswith how it's used to getthe tridiag. matrix.

:bB.t.w., the algorithm calculates up to v[m+1], I think this could be avoided. (also, "unrolling" the 1st part of the m=1 case as initialization should allow to avoid using v[0].) &mdash; [[User:MFH|MFH]]:[[User talk:MFH|Talk]] 03:09, 11 September 2008 (UTC)

:PS: also, it should be said what is 'm'...