nonuniform

Nonuniform is an adjective used to describe something that is not uniform; its properties, spacing, or values vary across space, time, or context rather than remaining constant or identical everywhere. The term is used across many disciplines, including mathematics, physics, engineering, statistics, and computer science.

In mathematics, nonuniform can describe phenomena whose regularity does not hold uniformly. For example, a sequence of functions may converge pointwise to a limit but fail to converge uniformly. Nonuniform convergence means that convergence behavior depends on the domain point, not the entire set.

In numerical analysis and computing, nonuniform grids or meshes use varying spacing to concentrate computation where the solution changes rapidly. This contrasts with uniform grids. Nonuniform grids are generated by transformations or adaptive refinement and are common in simulations, data interpolation, and spectral methods, including nonuniform fast Fourier techniques for irregular data.

In statistics and data collection, nonuniform sampling means that some regions or categories are sampled more densely than others, often to capture heterogeneity or rarity. Nonuniform distributions assign different probabilities to outcomes, unlike a uniform distribution where all outcomes are equally likely.