The Symbolic Toolbox for Interpolation with Wendlands Compactly Supported RBFs @JoelRosenfeld

Uploaded May 2021 | Updated September 2026, 1 day ago

This time around we use Wendland's compactly supported RBFs for interpolation. These RBFs are compact, which means that they can give sparse Gram matrices for interpolation, and the Hilbert space that they generate is norm equivalent to Sobolev spaces of certain degree.

To make them using MATLAB's symbolic toolbox, which uses symbolic variables, antiderivatives, substitutions, etc to build our RBFs. Finally, we demonstrate the effectiveness of these RBFs by interpolating the Franke function, a standard benchmark.

Code: bitbucket.org/joelrosenfeld/rbf-and-kernel-interpolation

Music:
Come 2gether by Ooyy
Sunrise in Paris by Dan Henig
Guardians + Tek by Craig Hardgrove

0:00 Start
6:50 MATLAB Start
9:44 Symbolic Toolbox and Wendland RBFs
20:00 Interpolation and Tuning the RBFs

The Symbolic Toolbox for Interpolation with Wendlands Compactly Supported RBFs

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The Symbolic Toolbox for Interpolation with Wendland's Compactly Supported RBFs