Bisection Method Algorithm

Bisection method is used for finding root of the function in given interval.

Algorithm:

IN:
Function f, which is continous function and interval [a,b]. Function must satisfy given equation: f(a) * f(b) < 0 - signs of that values are different, which means that given function in given interval has at least one root in interval [a,b].
OUT: 
Root in given interval.
1. Calculate c - midpoint of given interval using formula: c = (a + b) / 2.
2. Calculate f(c).
3. If b - a is small enough or abs(f(c)) is small enough: return c - which is the root we were searching for;
4. If(f(a) * f(c) < 0) assign c to b, else assign c to a.
5. Go to step 1.

Step By Step:

Sample Output:

f(x) = x * (x * (x * (x * (x)) + 2)) - 2
[0,2]

root: 0.8515625

Bisection Method Step By Step

Iteration Number	a	c	b	f(cn)
1	0	1	2	1
2	0	0.5	1	-1.4375
3	0.5	0.75	1	-0.55859375
4	0.75	0.875	1	0.117431640625
5	0.75	0.8125	0.875	-0.2438812255859375
6	0.8125	0.84375	0.875	-0.0693502426147461
7	0.84375	0.859375	0.875	0.022470533847808838
8	0.84375	0.8515625	0.859375	-0.023827489465475082

Pros:

• easy to implement.
• no need to calculate derivative of given function.

Cons:

• slow compared to other methods.

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