Is this a correct use of the phrase "iterate over'?
In Section Three, we briefly iterate over related work.
I disagree with both Rory Alsop's and Blessed Geek's answers.
The primary meaning of iterate (and reiterate) is "To say, mention, or assert again or repeatedly; to repeat." (OED). It had a former meaning "To do (something) over again; to perform (an action) a second time, or reproduce (an effect); to repeat; to renew.", which the OED marks as "now rare".
It is certainly the case that among software people, it has acquired a more general meaning of repeating a process exactly until some condition is met, or repeating a process on each member of some set of data; but I believe that this meaning is jargon, and will not necessarily be understood by people who are not familiar with software.
While I more or less understand what you mean, I find the word inappropriate, because to me it says that you are going to methodically do exactly the same thing to each bit of the work.
Iterate is to repetitively perform a task. If the task is transitive (i.e. has a target) over a range of targets, then we would need to say, iterate a task over that range of targets. i.e., to repetitively perform that task over a range of targets.
tr.v. it·er·at·ed, it·er·at·ing, it·er·ates
To say or perform again; repeat. See Synonyms at repeat.
[Latin iterre, itert-, from iterum, again; see i- in Indo-European roots.]
In algorithms and Mathematics, we would say iterate a task over a set. Where the set could be a collection of discrete items, or a continuous space.
For example, to iterate an evaluation task over a collection of one hundred stocks, at 1 minute intervals, would be to repetitively monitor the value of each of the stocks every minute.
Sometimes iterate is used in malapropism in place of reiterate. Reiterate is to repeat one or more time.
The difference between iterate and reiterate, is that reiterate can mean either
Whereas, iterate only means
Both iterate and reiterate would use the preposition over, when applied to a collection of targets. However, the preposition is often dropped when applied to an aggregation:
I wish to reiterate the need of contributing from each of you.
She had reiterated the weakness of the team.
We hope to reiterate over every student's need to contribute.
We need to reiterate over all the weaknesses of the team.
Reiterate normally imbues importance to the collection being reiterated over - where the collection is of such importance that we need to go over it one more time or repeatedly to make it sink in.
However, iterating over a collection (or set) would grammatically imbue more of a chore than importance to the collection/set.
Next time, when you hear or notice someone use the word iterate, kindly inquire that person if reiterate would be more appropriate. I suspect in the sentence which you supplied, the speaker/writer had actually meant reiterate.