Bisection<-function(func,x_left,x_right,accurary=0.001)
{
    if (f(x_left) * f(x_right)>0){
        cat("Two end points have the same sign! Cannot use bisection\n")
        return
    }
    iter = 1
    while(x_right-x_left>accurary)
    {
        x_mid = (x_left+x_right)/2
        cat("Iteration ", iter, " x=", x_mid, "\n");
        iter=iter+1
        if (f(x_mid)*f(x_left)>0) { #mid has same sign as left, then search right
            x_left = x_mid
        } else {
            x_right = x_mid
        }
    }
}
Newton <-function(func, funcPrime, x ,accurary=0.001)
{
    x_old = x
    iter = 1
    while(TRUE)
    {
        x_new = x_old - func(x_old)/funcPrime(x_old)
        cat("Iteration ", iter, " x=", x_new, "\n");
        if (abs(x_new - x_old)<accurary) {
            break;
        }
        if (abs(x_new-x_old)>1000) {
            cat("Newton's method seems to diverge\n");
            break;
        }
        if (iter>1000) {
            cat("No solution after 1000 iterations.\n");
            break;
        }
        x_old = x_new
        iter = iter+1
    }
}
f<-function(x) {return(x^3-x-2)}
fprime<-function(x) {return(3*x^2-1)}
Bisection(f,0,1)
Newton(f,fprime,2)
Newton(f,fprime,0)