Iterate
From Encyclopedia of Mathematics
The result of repeated application of a mathematical operation. Thus, if
 |
is a function of 
, then the functions
 |
are called the second
-th iterates of 
. E.g., putting 
one obtains
 |
 |
 |
The index 
is called the exponent of the iterate, while transition from 
to 
is called iteration. Iterates with an arbitrary real, or even complex, exponent can be defined for certain classes of functions. Iterates are used in the solution of various kinds of equations and systems of equations by iteration methods. For more information, see Sequential approximation, method of.
References
| [1] | L. Collatz, "Funktionalanalysis und numerische Mathematik" , Springer (1964) |
How to Cite This Entry:
Iterate. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Iterate&oldid=41854
Iterate. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Iterate&oldid=41854
This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article