I want to know what is the definition of rate of convergence (non-asymptotic) of iterative methods ?For example is it true that if $\|x_n - x^*\| \leq \frac{K}{n}\|x_0 - x^*\|$ then the rate of convergence is $O(1/n)$. 
Non-asymptotic rate of convergence of iterative methods
terminology;numerical algorithms