Chord Method Algorithm

Chord 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 x = (a * f(b) - b* f(a)) / (f(b) - f(a));
2. Check if abs(f(x)) < precision.
3. If it is end algorithm and return x.
4. Check if f(a) * f(x) < 0.
5. If it is make x = (x * f(a) - a* f(x)) / (f(a) - f(x)).
6. Else make x = (x * f(b) - b * f(x)) / (f(b) - f(x)).
7. Go to step 2.

Sample Output:

f(x) = x * (x + 2) -1
[-3, 0]

root: -2.414201183431953

Chord Method Step By Step

Iteration Number	a	b	x	f(xn)
1	-3	0	-1	-2
2	-3	0	-2	-1
3	-3	0	-2.3333333333333335	-0.22222222222222188
4	-3	0	-2.4	-0.04000000000000026
5	-3	0	-2.4117647058823533	-0.006920415224912602
6	-3	0	-2.413793103448276	-0.0011890606420928984
7	-3	0	-2.4141414141414144	-2.0406081012080968E-4
8	-3	0	-2.414201183431953	-3.501277966366789E-5

Pros:

• easy to implement.
• faster than bisection method.
• no need to calculate derivative of given function.

Cons:

• has trouble with some functions.

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