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Fast and stable rational RBF-based partition of unity interpolation. (English) Zbl 1524.65075

Summary: We perform a local computation via the Partition of Unity (PU) method of rational Radial Basis Function (RBF) interpolants. We investigate the well-posedness of the problem and we provide error bounds. The resulting scheme, efficiently implemented by means of the Deflation Accelerated Conjugate Gradient (DACG), enables us to deal with huge data sets and, thanks to the use of Variably Scaled Kernels (VSKs), it turns out to be stable. For functions with steep gradients or discontinuities, which are truly common in applications, the results show that the new proposed method outperforms the classical and rescaled PU schemes.

MSC:

65D12 Numerical radial basis function approximation
41A05 Interpolation in approximation theory
41A30 Approximation by other special function classes
65D15 Algorithms for approximation of functions
65D17 Computer-aided design (modeling of curves and surfaces)
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