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Calculs d'originaux par la méthode des résidus

English translation: calculation of originals with the residual method

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GLOSSARY ENTRY (DERIVED FROM QUESTION BELOW)
French term or phrase:Calculs d'originaux par la méthode des résidus
English translation:calculation of originals with the residual method
Entered by: Eric Heuberger
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22:21 Nov 10, 2008
French to English translations [PRO]
Tech/Engineering - Mathematics & Statistics / discrete-time signals
French term or phrase: Calculs d'originaux par la méthode des résidus
Application of Taylor series, sequences for the solution to differential equations, etc...

I appreciate all contributions from translators who are literate in math!
Eric Heuberger
United States
Local time: 01:21
calculation of originals with the residual method
Explanation:
Apparently there are at least two residual methods: weighted (pondérée) and generalized minimal (généralisée à minima)

In mathematics, the generalized minimal residual method (usually abbreviated GMRES) is an iterative method for the numerical solution of a system of linear equations. The method approximates the solution by the vector in a Krylov subspace with minimal residual. The Arnoldi iteration is used to find this vector.
The GMRES method was developed by Yousef Saad and Martin H. Schultz in 1986.[1]
http://en.wikipedia.org/wiki/GMRES

L'algorithme de GMRES est essentiellement une méthode des résidus minima: il con ..... Brown et Saad [B3] ont démontré que si Jn est non singulière et si le ...
ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-1234.pd... -


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Note added at 9 hrs (2008-11-11 08:03:37 GMT)
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Yes, forgot to say I had no idea about "calcul d'originaux"!
Selected response from:

xxxBourth
Local time: 01:21
Grading comment
Thank you very much.
4 KudoZ points were awarded for this answer

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Summary of answers provided
4Integration by the method of residues
chris collister
3integration by residues
a05
3calculation of originals with the residual methodxxxBourth


  

Answers


1 hr   confidence: Answerer confidence 3/5Answerer confidence 3/5
calculation of originals with the residual method


Explanation:
Apparently there are at least two residual methods: weighted (pondérée) and generalized minimal (généralisée à minima)

In mathematics, the generalized minimal residual method (usually abbreviated GMRES) is an iterative method for the numerical solution of a system of linear equations. The method approximates the solution by the vector in a Krylov subspace with minimal residual. The Arnoldi iteration is used to find this vector.
The GMRES method was developed by Yousef Saad and Martin H. Schultz in 1986.[1]
http://en.wikipedia.org/wiki/GMRES

L'algorithme de GMRES est essentiellement une méthode des résidus minima: il con ..... Brown et Saad [B3] ont démontré que si Jn est non singulière et si le ...
ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-1234.pd... -


--------------------------------------------------
Note added at 9 hrs (2008-11-11 08:03:37 GMT)
--------------------------------------------------

Yes, forgot to say I had no idea about "calcul d'originaux"!

xxxBourth
Local time: 01:21
Native speaker of: Native in EnglishEnglish
PRO pts in category: 29
Grading comment
Thank you very much.
Notes to answerer
Asker: Thanks. Your explanation proved quite helpful in establishing a consensus on an apparently quite academic term (although it seems that math is classically academic). Thank you.


Peer comments on this answer (and responses from the answerer)
neutral  chris collister: Oh dear. I think your answer is incorrect. I have used (Cauchy's) method of residues/contour integration for complex integrals many times. Vide Google. Note that "residue" has different meanings according to context
8 hrs
  -> That's entirely possible! I'm by no means a mathematician!
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9 hrs   confidence: Answerer confidence 4/5Answerer confidence 4/5
Integration by the method of residues


Explanation:
The method of residues was discovered by Cauchy over 100 years ago, and involves integrating a complex (ie with real and imaginary parts) function along a closed path. Its simplicity is so startling I practically fell off my chair when I came across it over 30 years ago!

chris collister
France
Local time: 01:21
Specializes in field
Native speaker of: Native in EnglishEnglish
PRO pts in category: 67
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8 hrs   confidence: Answerer confidence 3/5Answerer confidence 3/5
integration by residues


Explanation:
http://www.physics.miami.edu/~korotkova/PHY615_Lecture8.pdf

Calculs d'originaux is a French term for integration.

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Note added at 2 days7 hrs (2008-11-13 06:17:39 GMT) Post-grading
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You are right that this term can be found only in French cirriculums of the 1st year maths. This is the lead to its context, integration. Two functions are involved, "primitive" and "derivative". Integration is a procedure of finding the primitive (which they mean by "original") once its derivative is given. In more conventional language, the primitive is the integral. I strongly believe that "calculation of originals" will never prompt the right idea (integration) to an English-speaking mathematician.

Regarding Google, I am old enough to remember that paper textbooks also contain some wisdom, not necessarily found in Google. If one has time one may try to find our who used what set of terms among the founders of this science (Newton, Leibnitz, Cauchy, etc.), poor guys who had to do without Google.

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Note added at 2 days7 hrs (2008-11-13 06:18:35 GMT) Post-grading
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find out


    Reference: http://en.wikipedia.org/wiki/Residue_theorem
    Reference: http://www.jstor.org/pss/2028267
a05
Native speaker of: Native in RussianRussian
PRO pts in category: 4
Notes to answerer
Asker: Your answer was quite good, but I went with the order in which they came in, to be mathematical about it.


Peer comments on this answer (and responses from the answerer)
neutral  Nihil Credo: Had you seen the phrase "calculs d'originaux" used with that meaning before? I had never heard of it, and it has barely any Google hit.
4 hrs
  -> see comments
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