The regularizing properties of anisotropic radial basis functions |
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Authors: | G Casciola LB Montefusco S Morigi |
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Institution: | aDepartment of Mathematics, University of Bologna, P.zza di Porta San Donato 5, 40127 Bologna, Italy |
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Abstract: | In the present work we consider the problem of interpolating scattered data using radial basis functions (RBF). In general, it is well known that this leads to a discrete linear inverse problem that needs to be regularized in order to provide a meaningful solution. The work focuses on a metric-regularization approach, based on a new class of RBF, called anisotropic RBF. The work provides theoretical justifications for the regularization approach and it considers a suitable proposal for the metric, supporting it by numerical examples. |
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Keywords: | Radial basis functions Interpolation Regularization Ill conditioning |
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