Dyadic Intervals
A dyadic interval is a bounded real interval whose endpoints are and, where and are integers. Depending on the context, either endpoint may or may not be included in the interval.
Dyadic intervals have some nice properties, such as the following:
- The length of a dyadic interval is always an integer power of two.
- Every dyadic interval is contained in exactly one "parent" dyadic interval of twice the length.
- Every dyadic interval is spanned by two "child" dyadic intervals of half the length.
- If two open dyadic intervals overlap, then one of them must be a subset of the other.
The dyadic intervals thus have a structure very similar to an infinite binary tree.
Dyadic intervals are relevant to several areas of numerical analysis, including adaptive mesh refinement, multigrid methods and wavelet analysis. Another way to represent such a structure is p-adic analysis (for p=2).
Read more about this topic: Interval (mathematics)
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