# Positive constrained approximation via RBF-based partition of unity method

## TL;DR

This paper introduces a local, positive-constrained RBF-based partition of unity method that improves accuracy in constructing positive interpolants, with applications demonstrated in population dynamics.

## Contribution

It presents a novel local approach using PU techniques for positive RBF interpolation, avoiding restrictions to CSRBFs and optimizing constraints via error estimates.

## Key findings

- Enhanced accuracy through local constraints
- Effective in population dynamics applications
- Flexible approach not limited to CSRBFs

## Abstract

In this paper, we discuss the problem of constructing Radial Basis In this paper, we discuss the problem of constructing Radial Basis Function (RBF)-based Partition of Unity (PU) interpolants that are positive if data values are positive. More specifically, we compute positive local approximants by adding up several constraints to the interpolation conditions. This approach, considering a global approximation problem and Compactly Supported RBFs (CSRBFs), has been previously proposed. Here, the use of the PU technique enables us to intervene only locally and as a consequence to reach a better accuracy. This is also due to the fact that we select the optimal number of positive constraints by means of an a priori error estimate and we do not restrict to the use of CSRBFs. Numerical experiments and applications to population dynamics are provided to illustrate the effectiveness of the method in applied sciences.