Parametrizált

Parametrizált is the Hungarian adjective meaning parameterized, describing objects, models, or representations that are defined or described using one or more parameters. In mathematical and scientific contexts, the noun form parameterization (parametrizáció in Hungarian) refers to the process or result of introducing parameters to describe a structure.

In geometry, a curve, surface, or higher-dimensional object can be parametrized by a mapping from a parameter domain to the object. For example, a circle of radius r can be parametrized by x = r cos t, y = r sin t, where t is the parameter. A surface may be written as r(u, v) in terms of two parameters. A parameterization is often called regular if the derivative vectors with respect to the parameters are linearly independent; reparameterization changes only the parameter names, not the geometric object.

In statistics, a parametric family consists of distributions described by a finite set of parameters, such as the normal family described by the mean μ and standard deviation σ. Here, the model is parametrizált by those parameters, which determine its shape and location.

In computer science, engineering, and data modeling, parameterized models and algorithms use parameters to adapt to data, constraints, or design goals. Parameterization can lead to compact representations and easier analysis of variability, but may introduce identifiability or optimization challenges if different parameter values yield similar outcomes or if parameters are poorly constrained.

See also: parameterization, reparameterization.