Stepwise

Stepwise is an adjective used in English to describe procedures, processes, or objects that occur or proceed in small, discrete steps. In many disciplines, the term conveys an incremental approach, with results emerging step after step rather than in a single operation.

In mathematics and related fields, a stepwise function is a function defined by a sequence of intervals on which the function is constant or follows simple rules; step functions are a common example. A stepwise (or piecewise) function is constant on each interval with jump discontinuities and is used in modeling signals, distributions, and various numerical methods.

In statistics and data analysis, stepwise regression or stepwise model selection chooses predictors in a sequence determined by a criterion such as AIC, BIC, or p-values. Forward, backward, and combined (stepwise) procedures alternately add or remove variables. While simple to implement, these methods can lead to overfitting or biased estimates and do not guarantee finding the best model among all possible subsets.

In computing and software engineering, stepwise refinement is a design methodology in which a program is developed by progressively elaborating abstract steps into concrete, implementable components, preserving overall structure while increasing detail.

In music theory, stepwise motion describes moving from one note to the immediately neighboring scale degree, as opposed to leaping by larger intervals. Melodies with stepwise motion are typically smooth and connected, though many styles balance steps with larger leaps for variety.

In chemistry and biology, stepwise synthesis or stepwise processes refer to assembling complex molecules or procedures through discrete, manageable steps, each yielding a partially finished intermediate that is transformed further.

Across disciplines, stepwise describes any process carried out in stages, with meanings that adapt to the specific field.