What is the opposite to "discretization"?

Question

Solving an initially continuous problem using discrete math tools is known as "discretization".

Does the opposite option of using continuous tools to solve discrete problems have a name? And if not, is there any reason why?

Coming from natural language processing, that would apply for instance to resorting to word-embeddings, where one expresses words as vectors in order to escape from the essentially discrete nature of word combinatorics. In econometrics, that could apply to the standard modelling of discrete choices, where a fictional continuous quantity (utility) is maximised... and the list probably goes on for ever.

It is sometimes called extrapolation. I used to work in fixed-income derivatives and we would take a discrete (finite) set of bonds and generate a yield curve that was continuous. We referred to the operation as curve cooking. — John Douma, Aug 03 '22 at 14:13
One can consider iterating the time-$1$ map of a flow, as well as first return maps, as time discretizations. In this case the suspension construction could be considered as the opposite of time discretization. — Alp Uzman, Aug 03 '22 at 14:52
@user619894 There is not necessarily any idea of limit involved, as show the two exemples I mentioned. — Arthur, Aug 03 '22 at 16:06
In the context of Shannon sampling theorem it is interpolation — reuns, Aug 03 '22 at 16:59
@reuns I guess that interpolation indeed covers a large class of "continualization" techniques. — Arthur, Aug 04 '22 at 09:58

Claude COULOMBE · Answer 1 · 2022-09-12T13:17:31.927

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It seems to be an embedding as you already wrote. Check this Wikipedia entry: https://en.m.wikipedia.org/wiki/Embedding

The function or process could be called embedding or maybe continuity approximation.

edited Sep 12 '22 at 13:17

answered Sep 12 '22 at 13:08

Claude COULOMBE

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this belongs in a comment – Max0815 Sep 12 '22 at 13:32

What is the opposite to "discretization"?

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