Polyharmonic spline

In mathematics, polyharmonic splines are commonly used radial basis functions which are of the form

$\phi(r) = \begin{cases} r^k & \mbox{with } k=1,3,5,\dots, \\ r^k \log r & \mbox{with } k=2,4,6,\dots \end{cases}$

[edit] Reference

Scott A. Sarra, "Integrated Multiquadric Radial Basis Function Approximation Methods", Computers and Mathematics with Applications, vol. 51, no. 8, pp. 1283–1296, April 2006.

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