Editing Discretization (section)

{{Short description|Conversion of continuous functions into discrete counterparts}}
[[Image:Finite element solution.svg|right|thumb|A solution to a discretized partial differential equation, obtained with the [[finite element method]].]]

In [[applied mathematics]], '''discretization''' is the process of transferring [[continuous function|continuous]] functions, models, variables, and equations into [[wikt:discrete|discrete]] counterparts.  This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers. '''Dichotomization''' is the special case of discretization in which the number of discrete classes is 2, which can approximate a continuous variable as a [[binary variable]] (creating a [[dichotomy]] for [[conceptual model|modeling]] purposes, as in [[binary classification]]).

Discretization is also related to [[discrete mathematics]], and is an important component of [[granular computing]].  In this context, ''discretization'' may also refer to modification of variable or category ''granularity'', as when multiple discrete variables are aggregated or multiple discrete categories fused.

Whenever continuous data is '''discretized''', there is always some amount of [[discretization error]]. The goal is to reduce the amount to a level considered [[wikt:negligible|negligible]] for the [[conceptual model|modeling]] purposes at hand.

{{Anchor|Discretization-quantization}} The terms ''discretization '' and ''[[Quantization (signal processing)|quantization]]''<!-- Do not tag bomb this link with {{dn}}; its target is at the intentional and appropriate level of polysemy. --> often have the same [[denotation]] but not always identical [[connotations]].<!-- If you need deeper exploration of this truth, you will need to go read about [[cognitive synonymy]] and the lack of it in natural language. --> (Specifically, the two terms share a [[semantic field]].) The same is true of [[discretization error]] and [[quantization error]].

Mathematical methods relating to discretization include the [[Euler–Maruyama method]] and the [[zero-order hold]].