In order to find a root of a polynomial equation
 |
(1)
|
consider the difference equation
 |
(2)
|
which is known to have solution
 |
(3)
|
where 
,
, ..., are arbitrary functions of 
with period 1, and 
, ..., 
are roots of (1). In order to find the absolutely greatest
root (1), take any arbitrary values for 
, 
, ..., 
. By repeated application of (2), calculate in succession
the values 
,
,
,
.... Then the ratio of two successive members of this sequence tends in general to
a limit, which is the absolutely greatest root of (1).
