拟牛顿法

    public static void sqrt1(double x){
        // 方法1, 拟牛顿近似法
        // x * x * x - N 
        // x1 = N ;

        // y - y1 = 3x1*x1(x - x1)
        // x1 = (3x1 * x1 * x1 - y1) / (3x1 * x1)

        // y1 = x1 * x1 * x1 - N

        // ===> x1 = (3x1 * x1 * x1 - x1 * x1 * x1 + N )/(3x1 * x1)
        // ===> x1 = (2 * x1 * x1 * x1 + N)/(3 * x1 * x1)
        double start = x;
        double delta = 1;
        while(delta > 1e-8 || delta < -1e-8){
            double y_next = x * x * x - start;
            double x_next = (2 * x * x * x + start)/(3 * x * x);
            delta = x - x_next;
            x = x_next;
        }

        System.out.printf("%.6f",x);
    }

二分法

    public static void sqrt2(double x){
        double l = -10000;
        double r = 10000;

        while(r-l > 1e-8){
            double mid = (l + r) / 2;
            if(mid * mid * mid >= x){
                r = mid;
            }else{
                l = mid;
            }
        }

        System.out.printf("%.6f", l);

    }