Adaptive residual subsampling methods for radial basis function interpolation and collocation problems
Radial basis functions are a useful tool for multivariable approximation and currently very popular for solving differential equations. The method of choice for this is collocation or interpolation, mostly for boundary value problems. Here, this approach is taken for both boundary and initial value problems, including the use of radial basis functions with parameters and knot removal. Mainly, so-called residual subsampling methods are employed. The condition numbers of the necessarily ensuing interpolation (collocation) matrices are also discussed and examples provided.
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