Table 1 [k] denotes the nearest integers less than or equal to k, and N the natural number, c a positive constant which is known as the shape parameter, and CPD denotes the m-order conditionally positive definite functions [3, 11]
Name of RBF | Definition | CPD order (m) |
|---|---|---|
Multiquadric (MQ) | ϕ(r,c)=(r2+c2)kifk>0, k∉N | [k]+1 |
Inverse multiquadric (IMQ) | ϕ(r,c)=(r2+c2)−kifk>0, k∉N | 0 |
Gaussian (GA) | \(\phi (r,c)=e^{\frac {-r^{2}}{c^{2}}}\) | 0 |
Polyharmonic spline | \(\phi (r) = \left \{ \begin {array}{lr} r^{2k-1} & if \quad k\in N\\ r^{2k-1}log(r) & if \quad k\in N.\\ \end {array} \right.\) | [k/2]+1 |
Thin plate splines (TPS) | ϕ(r)=r2ln(r) | 0 |