I'm not comfortable with math terms. " Iteration " can have some meanings :
- a repetition of an action (e.g. in a program)
- a different form or version of something
- a problem-solving or computational method in which a succession of approximations, each build on the preceding one , is used to achieve a desired degree of accuracy
I would like to use " iteration " in the first sens I itemize (repetition of a process). Am I right ?
It means executing or continuing the same set of instructions or commands a given number of times or until a specified result is obtained.
I would say that your usage is correct in non technical English, while the standard meaning in numerical mathematics (at least) is the third item on your list. Performing the same action on different operands (not being each the output of the previous action) is not understood as iteration, but rather repetition.
Thank you Renosh and Luca for your answers.
The use of "iteration" is really dependent on the topic. I'll use "repetitive process" rather than iterative process to avoid confusion.
The meaning of iteration I know is specific to dynamical systems theory and goes back to Poincaré: you have a map, namely a way to associate a point to another point (in a plane for instance. You take the result of the first map as the entry of the map and continue. One of the best known iteration is given by Hénon's map (from two dimensions to two dimensions). It is still unproved that the result of Hénon's iteration is, for an arbitrary initial point, a set of random point. In general it is extremely hard to show that the outcome of such iterations are random whereas this randomness shows up in computer studies.
Dear Yves. Thank you for your precision about the origin. I realized that my use of the word "iteration" is totally mistaken. In non-mathematician terms, I already found this word in the context of "repetitive process". My goal isn't to offend mathematicians !
Anne-Hélène
Repetitive action either computation to improve accuracy or include synonyms for better understanding..
Thank you all for your answers.
I've consulted the website of wikipedia for the definition but, for a non-native speaker and non-mathematician, it is difficult to make a well-considered decision.
So, "iteration" has the three definitions I listed; but in Mathematics, the third sens is the more common. In a multi-domain science, can I use "loop-process" to replace the word iteration? Or is it too much informal?
Everything we do are iteration only - we never reach the coveted ideal state :-))
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