Title: GPU-Accelerated Scattered Data Fitting with Optional Monotonicity Constraints: The LipFit Package

Abstract:

This study introduces a technique for the interpolation and approximation of multivariate scattered data that generates an optimal Lipschitz-continuous solution while adhering to specified monotonicity requirements. The proposed method utilizes precise upper and lower bounds to approximate the dataset. Conceptually, it shares similarities with nearest-neighbor approaches but avoids the associated discontinuities. Additionally, the paper details techniques for local Lipschitz interpolation and smoothing. As an instance-based approximation strategy that requires no training period, this approach is inherently well-suited for parallelization on GPUs. Finally, the authors introduce LipFit, a Python package designed for GPU compatibility that implements these discussed methodologies.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC