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Positive constrained approximation via RBF-based partition of unity method. (English) Zbl 1360.65047

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.

MSC:

65D05 Numerical interpolation
92D25 Population dynamics (general)

Software:

rbf_qr; Matlab; QSHEP3D
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Full Text: DOI arXiv

References:

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