For a parameterized hyperbolic system $u_{ i+1} = f(u_i,s)$, the derivative of an ergodic average $\ < J\ > = \underset{ n\rightarrow\infty}{ \lim} \frac1n \sum_1^n J(u_i,s)$ to the parameter $s$ can be computed via the least squares sensitivity method. This method solves a constrained least squares problem and computes an approximation to the desired derivative $d\ < J\ > \over ds$ from the solution. This paper proves that as the size of the least squares problem approaches infinity, the computed approximation converges to the true derivative.
Categories: math.DS