text: In numerical analysis, the order of convergence and the rate of convergence of a convergent sequence are quantities that represent how quickly the sequence approaches its limit. A sequence  that converges to  is said to have order of convergence  and rate of convergence  if
  The rate of convergence  is also called the asymptotic error constant.
  Note that this terminology is not standardized and some authors will use rate where
  this article uses order (e.g., ).
  In practice, the rate and order of convergence provide useful insights when using iterative methods for calculating numerical approximations. If the order of convergence is higher, then typically fewer iterations are necessary to yield a useful approximation. Strictly speaking, however, the asymptotic behavior of a sequence does not give conclusive information about any finite part of the sequence.