Effective H^{\infty} interpolation

Given a finite set \sigma of the unit disc $\mathbb{D}$={z\in$\mathbb{C}$:, |z|<1} and a holomorphic function f in $\mathbb{D}$ which belongs to a class X, we are looking for a function g in another class Y (smaller than X) which minimizes the norm |g|{Y} among all functions g such that g{|\sigma}=f_{|\sigma}.