Polyharmonic spline

Polyharmonic splines are used for function approximation and data interpolation. They are very useful for interpolating and fitting scattered data in many dimensions. A special case is the thin plate spline.

A polyharmonic spline is a linear combination of polyharmonic radial basis functions (RBFs) denoted by ${\displaystyle \phi }$ plus a polynomial term:

${\displaystyle f(\mathbf {x} )=\sum _{i=1}^{N}w_{i}\phi (|\mathbf {x} -\mathbf {c} _{i}|)+\mathbf {v} ^{\textrm {T}}{\begin{bmatrix}1\\\mathbf {x} \end{bmatrix}}}$

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