Let's consider the equation (1):
where
The last means, that function
We halve the segment. If
, then
is the root of the equation (1). If
, then we consider that half of the segment
on which ends function
such, that (9) and (10) The left ends of these segments form the monotonous (not decreasing) limited sequence, and the right ends – the monotonous (not increasing) limited sequence. Therefore by equality (10) there is a general limit
Passing in (9) to a limit at
, by continuity of the function
In practice the process (10) is considered completed, if (11) where – the given accuracy of solution. |

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>> Numerical Methods
>> Algebraic and Transcendental Equations
>> Method of halving