Suppose i have a function f defined on the positives reals that i can only evaluate values from : for a given x, i have an algo that compute f(x) but that's it (and it's costly..)
I want to approximate by another function $g$ with parameters a_i and b_i and the following form :
g(x) = sum_{i=1}^n [ a_i/(b_i - x) ]
For a given number n of couples (a_i,b_i).
What algorithm could i use to do such thing ?