I have to design a matrix A that solves a linear system:
$=$, where x is a known complex vector and y is a known complex vector.
The requirement is that A is an RBF kernel, i.e., it has the following structure:
$a_{ij} = \alpha \, \exp\left (\frac{-d_{ij}^2}{2\sigma^2}\right)$, where d is the distance between each element in the matrix.
I need to find at least one example of A. $\sigma $ and $\alpha$ can be whatever.
Any ideias?
Luisa.