User talk:CyrilleDunant: Difference between revisions

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Cholesky decomposition

Hello. I am a bit puzzled by your changes to Cholesky decomposition. Why do you want to write A = LL^T instead of A = LL^*? Indeed, if A is real then L is also real and the transpose is the same as the conjugate transpose, in which case I can see that you prefer the first expression. However, if A is complex then this is no longer true, and you have to use the conjugate transpose. Or am I missing something? -- Jitse Niesen (talk) 20:11, 14 August 2005 (UTC)

well, technically, A has to be symetric positive. so "pure" Cholesky decomposition is really "real". But a section saying the concept is extensible in $\mathbb {C}$, using the conjugate transpose would be good. Also -- but this is nitpicking -- this is really useful in numerics, and though you can make calculations on complex, you avoid them as much as possible for performance reasons... CyrilleDunant 05:42, 15 August 2005 (UTC)

What do you mean with "technically, A has to be symmetric positive"? Why not Hermitian and positive definite? I agree with your last comment, which is why I didn't complain when you replaced conjugate transpose with transpose in the section on solving equations. There may well be a pedagogical value in first assuming that A is real and then extending to the complex case, but it seems you have a different reason in mind. -- Jitse Niesen (talk) 11:44, 15 August 2005 (UTC)

I must confess I am seeing Cholesky decomposition from a very numerical point of view. Which means that for all practical purposes A _is_ real (and symmetric and positive defined (hmmm, doubt on the english term... I mean "all eigenvalues are strictly positive")). That it is extensible to $\mathbb {C}$ is obvious if you have seen once in your life a complex. So if you feel that the T version is in essence wrong, well, revert. I don't care much :)

Since you seem to be knowledgable, wouldn't it work also with quaternions? CyrilleDunant 05:43, 16 August 2005 (UTC)

I'll check some books first, just to be sure. I have no idea whether it works with quaternions; I've never used those. By the way, I'm one of those rare people who do use complex numbers in numerical computations. The English term is "positive definite". -- Jitse Niesen (talk) 10:34, 16 August 2005 (UTC)

That's interesting, don't you get quite a performance hit? what do you use them for ? My "specialty" is FEM for microstructures, and I'm always happy to learn new efficient techniques...

I'm solving ODEs with a parameter which takes complex values (in particular, I'm not using the Cholesky decomposition). Of course it's more expensive to use complex numbers instead of reals, and as you say, you try to avoid them, but if the problem has complex variables in it, you have to use complex arithmetic.

I did mention complex numbers again in the Cholesky decomposition article, but the stress is still on real matrices. I am wondering though whether the Cholesky decomposition is used outside numerical analysis. -- Jitse Niesen (talk) 17:16, 17 August 2005 (UTC)

I like the latest revision. I think it really makes sense this way.

Eurofighter

Thanks for catching that edit. I'm sure the person has a genuine objection but in that case I can't understand why they wouldn't create an account and discuss it! It's not perfect, but as I said in the edit summary they are reputable sources. Thanks again. Mark83 15:43, 23 February 2006 (UTC)

Also, it is clearly stated that the numbers are somewhat speculative. So the current setup seemed to me accurate and honest. So I reverted :) CyrilleDunant 16:12, 23 February 2006 (UTC)

BAE released there first formal report today since the deal (2005 Preliminary Report) and it says:

"It is... intended that Typhoon aircraft will replace Tornado Air Defence Variant aircraft and other aircraft in service with the Royal Saudi Air Force. The details of these arrangements are confidential."

So I think the current format is the best we're going to get for a while! Thanks again. Mark83 23:40, 23 February 2006 (UTC)

US/British English - Airbus A400M

What on earth are you doing changing Boeing Integrated Defense Systems to Boeing Integrated Defence Systems? It is wrong in every way. Primarily of course because the first article exists and the second does not! Not a very productive edit in that sense. Also it is a company registered in the United States, so you cant just change it to meet your preferences, they could register as Boeing Integrated Defennnnnnnnse Systems and we would still be obliged to link to it. Mark83 11:41, 19 June 2006 (UTC)

Ooops sorry, knee-jerk reaction -- actually, I wondered. Should have checked...:)

Mediation

The announced mediation, concerning the Charlemagne article, will take place soon, you are invited to participate. See: Wikipedia:Requests for mediation

Rex 18:24, 7 July 2006 (UTC)