There are still people who like to Latinise their vocabulary to make up for not really having anything worthwhile to say and I bet they'd pick up the word "Amelioration" if you showed it to them. There's a general trick that you can import Latinate English vocabulary into German and pronounce it German to sound obnoxiously pretentious (e.g. apparently the official German phrase for "lift boy" is "Elevatorführer" which sounds so pretentious to Germans that most people I've pointed this out to thought it was satire).

That said, "Analysis" is a distinct term in mathematics (I think the meaning is the same in English in that context). Outside of mathematics it is actually "Analyse" (such as when analysing a substance in chemistry or inspecting something in close detail in general). I don't think "Zerlegung" is particularly widely used in any context but it might be.

I was a bit confused when I began studying computer science in university because all my prior exposure to programming had been colloquial or in English. But German academia had actually created its own vocabulary for things like stacks ("Stapel") and arrays ("Felder"), which are mostly just exact translations. This seems particularly awkward when nearly all actual programming is done in English and the academic and practical vocabulary clashes so hard.