Bounds on the Number of Pieces in Continuous Piecewise Affine Functions
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Abstract (arXiv)
The complexity of continuous piecewise affine (CPA) functions can be measured by the number of pieces p or the number of distinct affine functions n. For CPA functions on ℝd, this paper shows an upper bound of p=O(nd+1) and constructs a family of functions achieving a lower bound of p=Omega(n^d+1-fracc√log2(n)).
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). First posted on arXiv 12 Mar 2025.
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2 papers.