text: The sequence also converges linearly to 0 with rate 1/2 under the R-convergence definition, but not under the Q-convergence definition. (Note that  is the floor function, which gives the largest integer that is less than or equal to .)
  The sequence
  converges superlinearly. In fact, it is quadratically convergent.
  Finally, the sequence
  converges sublinearly and logarithmically.
  Convergence speed for discretization methods
  A similar situation exists for discretization methods designed to approximate a function , which might be an integral being approximated by numerical quadrature, or the solution of an ordinary differential equation (see example below).  The discretization method generates a sequence , where each successive  is a function of  along with the grid spacing  between successive values of the independent variable .  The important parameter here for the convergence speed to  is the grid spacing , inversely proportional to the number of grid points, i.e. the number of points in the sequence required to reach a given value of .
  In this case, the sequence  is said to converge to the sequence  with order q if there exists a constant C such that
  This is written as  using big O notation.
  This is the relevant definition when discussing methods for numerical quadrature or the solution of ordinary differential equations (ODEs).