Superlinear growth is growth of an eventually positive real-valued function 
faster than any constant multiple
of 
as 
tends to infinity. It is characterized by the limit
 |
Equivalently, 
in little-omega notation (Cormen et al.
2001, p. 48). The same definition applies to a sequence 
as 
.
For example, 
and 
for every fixed 
have superlinear growth. A linear function 
with 
has linear growth instead,
since its ratio to 
is the constant 
. Superlinear growth need not be bounded below by 
for any fixed 
and 
. In particular, 
grows more slowly than every such power, since 
for every fixed 
.
This meaning is distinct from superlinear convergence, which concerns the decrease of errors in a convergent sequence.
