Parametrisera

Parametrisera is a Swedish verb meaning to describe or express something using parameters, or to convert a description that relies on explicit quantities into a parameterized form. The term is formed from parameter and the suffix -isera, indicating the act of making something parameter-driven. In technical contexts, to parameterize a model or a relation is to introduce one or more variables that capture degrees of freedom, allowing adjustments without changing the underlying structure.

In mathematics, a curve, surface, or function can be parameterized by a parameter or a set of parameters. For example, a curve can be described by x = f(t), y = g(t) with t ranging over an interval, instead of an implicit equation relating x and y. In computer science and engineering, parameterization is used to create models, algorithms, or simulations that can be tuned by changing parameters rather than rewriting code. In statistics and data science, a parametric model is defined by a finite set of parameters, such as a normal distribution with parameters μ and σ.

Common examples include the parameterization of a circle by x = r cos t and y = r sin t (t in [0, 2π)), or a line described by x = x0 + a t, y = y0 + b t. Parameterization facilitates sampling, optimization, and sensitivity analysis, and it contrasts with non-parametric approaches that do not assume a fixed finite set of parameters. The term is widely used in mathematics, physics, computer science, and related fields.