Positive constrained approximation via RBF-based partition of unity method

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...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2017-08, Vol.319, p.338-351
Main Authors: De Rossi, Alessandra, Perracchione, Emma
Format: Article
Language:English
Subjects:
Applications to population dynamics
Constrained approximation
Meshfree approximation
Partition of unity method
Positivity-preserving property
Radial basis functions
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Summary: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 in Wu et al. (2010). 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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2017.01.024