linearisere

Linearisere is a verb used in Norwegian and Danish to mean to linearize. It denotes the act of approximating or transforming a nonlinear relation, model, or dataset into a linear form. Etymology derives from linear and the -ere suffix typical of infinitive forms in those languages; in English the related term is linearize.

In mathematics, linearisering around a point x0 means approximating a nonlinear function f near x0 by its tangent linear function: f(x) ≈ f(x0) + f'(x0)(x − x0). In multiple dimensions this generalizes to f(x) ≈ f(x0) + ∇f(x0)·(x − x0). This local linear approximation captures small deviations from the operating point.

In applied sciences, linearisering is used for small-signal analysis in control theory and dynamical systems, where a nonlinear system is replaced by its linear counterpart based on the Jacobian evaluated at an operating point. This enables the use of linear system tools to study stability, frequency response, and controllability.

In statistics and data analysis, linearisering can refer to transforming a nonlinear relationship to improve linear fit, using methods such as logarithmic or power transformations (e.g., Box-Cox) to stabilize variance or achieve linearity for linear regression.

The term is most common in Scandinavian technical writing and in contexts where English uses linearize but a native language version exists. In English texts, linearisere is often encountered as a loanword or in translations of Scandinavian sources.