  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.
