Newton Method Algoritm

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

Algorithm:

IN: 
Function f, which is continous function and value: a - being intital guess - the closer to root, the better. Function fD, which is the derivative of function f.
OUT: 
Root in given interval.
1. Make x = a and prevX = a.
2. Check if abs(f(x)) < precision.
3. If it is end algorithm and return x.
4. Make x = prevX - (f(prevX) / fD(prevX)).
5. Make prevX = x.
6. Go to step 2.

Sample Output:

f(x) = x * (x + 2) -1
-3

root: -2.414201183431953

Iteration Number	a	prevX	x	f(x)
1	-3	-3	-3	2.0
2	-3	-3	2.5	0.25
3	-3	2.5	-2.416	0.0069
4	-3	-2.416	-2.414	6.007E-6

Pros:

• easy to implement (without approximating the derivative of function!).
• very fast method (not counting some special functions).
• no need to find initial interval, simply choose a number and one of the roots should be found.

Cons:

• has trouble with some functions.
• If a stationary point of given function is encountered, there will be devision by zero, because of the derivative being zero.
• need to calculate derivative of given function.
• may miss root.

 

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