Question

i have posted a few hours ago question about newtons method,i got answers and want to thanks everybody,now i have tried to implement code itself

#include <iostream>
#include <math.h>
using namespace std;
#define h powf(10,-7)
#define PI 180
float funct(float x){

    return cos(x)-x;


}
float derivative (float x){
    return (( funct(x+h)-funct(x-h))/(2*h));

}
int main(){
    float tol=.001;
    int N=3;
    float p0=PI/4;
    float p=0;
    int i=1;
    while(i<N){

        p=p0-(float)funct(p0)/derivative(p0);
        if ((p-p0)<tol){
            cout<<p<<endl;
            break;

        }


        i=i+1;
        p0=p;


    if (i>=N){
        cout<<"solution not found "<<endl;
        break;
    }
    }



    return 0;
}

but i writes output “solution not found”,in book after three iteration when n=3 ,it finds solution like this .7390851332,so my question is how small i should change h or how should i change my code such that,get correct answer?

Answer 1

Several things:

1. 2 iterations is rarely going to be enough even in the best case.
2. You need to make sure your starting point is actually convergent.
3. Be aware of destructive cancellation in your derivative function. You are subtracting two numbers that are very close to each other so the difference will lose a lot of precision.

To expand on the last point, the general method is to decrease h as the value converges. But as I mentioned in your previous question, this “adjusting” h method essentially (algebraically) reduces to the Secant Method.