text: Similar concepts are used for discretization methods. The solution of the discretized problem converges to the solution of the continuous problem as the grid size goes to zero, and the speed of convergence is one of the factors of the efficiency of the method. However, the terminology, in this case, is different from the terminology for iterative methods.
  Series acceleration is a collection of techniques for improving the rate of convergence of a series discretization. Such acceleration is commonly accomplished with sequence transformations.
  Convergence speed for iterative methods
  Convergence definitions
  Suppose that the sequence  converges to the number . The sequence is said to converge with order  to , and with a rate of convergence of , if
  for some positive constant  if , and  if . It is not necessary, however, that  be an integer. For example, the secant method, when converging to a regular, simple root, has an order of φ ≈ 1.618.
  Convergence with order
  is called linear convergence if , and the sequence is said to converge Q-linearly to .
  is called quadratic convergence.
  is called cubic convergence.
  etc.
  Order estimation
  A practical method to calculate the order of convergence for a sequence generated by a fixed point iteration is to calculate the following sequence, which converges to :
  For numerical approximation of an exact value through a numerical method of order q see