Fitting scattered data with optional monotonicity constraints on GPU: LipFit package

Abstract:This paper presents a method of multivariate scattered data interpolation and approximation that produces optimal Lipschitz-continuous approximation, subject to the desired monotonicity constraints. This method relies on tight upper and lower approximations to the data, and is similar in its spirit to the nearest-neighbour approximation but does not suffer from discontinuities. Local Lipschitz interpolation and Lipschitz smoothing are also presented. This approach falls under the umbrella of instance-based approximation with no training phase, and it is suitable for GPU-based parallelisation. A Python GPU-friendly package LipFit which implements the methods discussed is discussed.

Numerical Analysis (math.NA); Machine Learning (cs.LG); Mathematical Software (cs.MS)

arXiv:2606.04670 [math.NA]

(or arXiv:2606.04670v1 [math.NA] for this version)

https://doi.org/10.48550/arXiv.2606.04670 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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