{"ID":3050134,"CreatedAt":"2026-06-04T02:13:16.786527022Z","UpdatedAt":"2026-06-06T08:58:50.400332682Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.04670","arxiv_id":"2606.04670","title":"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.","short_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-neigh...","url_abs":"https://arxiv.org/abs/2606.04670","url_pdf":"https://arxiv.org/pdf/2606.04670v1","authors":"[\"Gleb Beliakov\"]","published":"2026-06-03T09:51:56Z","proceeding":"math.NA","tasks":"[\"math.NA\",\"cs.LG\",\"cs.MS\"]","methods":"[]","has_code":false}