title: Big O of an algorithm that relies on convergence
body: <p>I'm wondering if its possible to express the time complexity of an algorithm that relies on convergence using Big O notation.</p>
  
  <p>In most algorithmic analysis I've seen, we evaluate our function's rate of growth based on input size.</p>
  
  <p>In the case of an algorithm that has some convergence criteria (where we repeat an operation until some defined error metric is below a threshold, or the rate at which the error metric is changing is below some threshold), how can we measure the time complexity? The number of iterations required to converge and exit that loop seems difficult to reason about since the way an algorithm converges tends to be dependent on the content of the input rather than just it's size.</p>
  
  <p>How can we represent the time complexity of an algorithm that relies on convergence in Big O notation?</p>