Newton's method for solving equations

1. Basic principles explained

 

 

2. Apply Newton iteration method to find the root number

  Find √a

  That is to solve the equation: x²-a = 0

   

 

 

#define ABS(val) (((val)>0)?(val):(-(val)))

double my_sqrt(double a)
{
    double k = 1.0;
    while(ABS(k*k-a)>1e-9) {
        k = (k+a/k)/2;
    }
    return k;
}