I consider a discrete non-linear dynamical system. I know it is asymptotically stable because all eigenvalues evaluated at the fix point have modulus less than one.
Now I am interested in the runtime.
Are the any techniques to obtain the runtime? Is the runtime related to the largest eigenvalue at the fix point?
By runtime I mean the number of iterations needed until being close to the optimal solution. I currently do not know how to quantify "close to an optimal solution", I am just interested if there are results known.