Table1 Types of infinitely smooth RBFs with \(\lambda > 0~{\text {and}} ~r \in x\)
From: A review of radial basis function with applications explored
RBFs | Definition |
|---|---|
Gaussian function (GS) | \(\varphi \left( r \right) = e^{{ - \left( {\lambda r} \right)^{2} }}\) |
Multi-quadric (MQ) | \(\varphi \left( r \right) = \sqrt {1 + \left( {\lambda r} \right)^{2} }\) |
Inverse multi-quadric (IMQ) | \(\varphi \left( r \right) = \frac{1}{{1 + \left( {\lambda r} \right)^{2} }}\) |
Inverse quadric (IQ) | \(\varphi \left( r \right) = \frac{1}{{\sqrt {1 + \left( {\lambda r} \right)^{2} } }}\) |