# 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:

 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 HeubergerUnited States Local time: 11:59
 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"!
Selected response from:

xxxBourth
Local time: 11:59
 Thank you very much. 4 KudoZ points were awarded for this answer

4Integration by the method of residues
 chris collister
3integration by residues
 a05
3calculation of originals with the residual method
 xxxBourth

1 hr   confidence:
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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 xxxBourthLocal time: 11:59Native speaker of: EnglishPRO pts in category: 29
 Thank you very much.

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!

9 hrs   confidence:
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 collisterFranceLocal time: 11:59Specializes in fieldNative speaker of: EnglishPRO pts in category: 67

8 hrs   confidence:
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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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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find out

Reference: http://en.wikipedia.org/wiki/Residue_theorem
Reference: http://www.jstor.org/pss/2028267
 a05Native speaker of: RussianPRO pts in category: 4

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

 Nov 10, 2008: Kudoz queue In queue » Public

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