intervalwise

Intervalwise is an adjective and adverb used to describe analysis, methods, or properties that are defined on intervals or applied to intervals rather than globally over an entire domain. The term is common in mathematical and computational contexts where locality or modularity is important.

In mathematics, intervalwise approaches appear in interval analysis and interval arithmetic, where numerical values are represented by intervals to capture uncertainty and arithmetic is performed intervalwise to produce result intervals. Intervalwise reasoning also appears in piecewise definitions and in discussions of convergence on subdomains, sometimes referred to as intervalwise or subinterval analysis.

In computer science and time-series processing, intervalwise processing refers to dividing input streams into fixed-length windows or blocks and applying computations within each block. This facilitates streaming algorithms, parallelization, and localized modeling. In scheduling and constraint programming, intervalwise constraints focus on time-aspect properties across intervals rather than a single time point.

The term reflects a broader family of ideas tied to locality, partitioning, and bounded analysis. While intervalwise methods are widely used in certain fields, there is no single formal theory named intervalwise. Depending on the context, intervalwise concepts may overlap with local analysis, segmentation, or windowed approaches.