text: Q-convergence definitions In addition to the previously defined Q-linear convergence, a few other Q-convergence definitions exist. Given Definition 1 defined above, the sequence is said to converge Q-superlinearly to  (i.e. faster than linearly) in all the cases where  and also the case . Given Definition 1, the sequence is said to converge Q-sublinearly to  (i.e. slower than linearly) if . The sequence  converges logarithmically to  if the sequence converges sublinearly and additionally if
  Note that unlike previous definitions,  logarithmic convergence is not called "Q-logarithmic."
  In the definitions above, the "Q-" stands for "quotient" because the terms are defined using the quotient between two successive terms. Often, however, the "Q-" is dropped and a sequence is simply said to have linear convergence, quadratic convergence, etc.
  R-convergence definition
  The Q-convergence definitions have a shortcoming in that they do not include some sequences, such as the sequence  below, which converge reasonably fast, but whose rate is variable. Therefore, the definition of rate of convergence is extended as follows.
  Suppose that  converges to . The sequence is said to converge R-linearly to  if there exists a sequence  such that
  and  converges Q-linearly to zero. The "R-" prefix stands for "root".
  Examples
  Consider the sequence
  It can be shown that this sequence converges to . To determine the type of convergence, we plug the sequence into the definition of Q-linear convergence,
  Thus, we find that  converges Q-linearly and has a convergence rate of .
  More generally, for any , the sequence  converges linearly with rate .