The convergence properties of an algorithm are described by two
analytic quantities: convergence * order* and convergence * ratio*.
A sequence is said to converge to if the
following holds: .
The sequence is said to converge to with * order* **p**
if **p** is the largest nonnegative number for which a finite limit
exists, where

When **p=1** and , the sequence is said to converge
* linearly* (e.g., for **n=1**); when **p=1**
and , the sequence converges * superlinearly* (e.g.,
); and when **p=2**, the convergence is * quadratic*
(e.g., ). Thus, quadratic convergence is more rapid
than superlinear, which in turn is faster than linear.
The constant is the associated convergence ratio.

(See exercise 6.)