I'm having troubles solving the following problem. I have 2 2D lookup tables of the form
$\lambda_1 = f_1(x, y) \\ \lambda_2 = f_2(x, y)$
where
$x\in \{x_1, x_2,...,x_N\}$ and $y\in \{y_1, y_2,...,y_M\}$
Essentialy $\lambda_1$ and $\lambda_2$ are MxN Real matrices (for completeness but not strictly necessary to the resolution of the problem, these are the fluxes of two non-linear magnetically coupled iron cores where 'x' is the current circulating of the first, 'y' is the current circulating on the second, $\lambda_1$ is the total flux-linkage on the 1st core and $\lambda_2$ is the total flux-linkage on the 2nd core).
I want to be able to find the inverse lookup tables such that
$x = g_1(\lambda_1, \lambda_2)\\ y = g_2(\lambda_1, \lambda_2)$
Feel free to ask for more details if the question is not clear enough. Thanks in advance for any help!