nth root by Newton’s method
The Newton’s method is very suitable for computing approximate values of higher roots (http://planetmath.org/NthRoot) of positive numbers (and odd roots of negative numbers!).
The general recurrence formula
of the method for determining the zero of a function , applied to
whose zero is , reads
For a radicand , beginning from some initial value and using (1) repeatedly with successive values of
, one obtains after a few steps a sufficiently accurate value of if was not very far from the searched root.
Especially for cube root , the formula (1) is
For example, if one wants to compute and uses , already the fifth step gives
|Title||nth root by Newton’s method|
|Date of creation||2013-03-22 19:09:38|
|Last modified on||2013-03-22 19:09:38|
|Last modified by||pahio (2872)|
|Synonym||cube root of 2|