Java 中的 Newton-Raphson 方法

Question

我正在编写一个程序以在 Java 中应用 Newton-Raphson 方法，其中包含一个方程：

f(x) = 3x - e^x + sin(x)

和

g(x) = f'(x) = 3- e^x + cos (x)

问题是当我试图解决论文中的方程以达到小于 (0.5%) 的误差
我得到了：

       Xn                          |错误

Xo = 2                      | ----------------------

X1 = 1.900158400          | 5.254%

X2 = 1.89012709            | 0.5307%

但是当我用 Java 编写程序时，它没有到达最后一行，这是必需的错误
（例如：X2 = 1.89012709）
它只显示第一行，即第一步
(X1 = 1.900158400)

我的 Java 代码是：

package newton.raphson.method;

public class NewtonRaphsonMethod {


          // let f be a function defined as f(x) = 3x - e^x + sin(x)

        public static double f (double x){

            return (3*x-(Math.pow(Math.E, x))+Math.sin(x));
        }

        // let g be a function defined as g(x) = f'(x) = 3- e^x + cos (x)


     public static double g (double x){

            return (3-(Math.pow(Math.E, x))+Math.cos(x));
        }


          public static double NewtonRaphson (){
              int iterations_number=0;
              boolean cont = true;
            double x0 , x1, Error=5000;
            x0 =2;
            x1=0;

            while (cont){
            x1 = x0 - (f(x0)/g(x0));
            Error = (Math.abs(x1-x0)/x1)*100;
            iterations_number++;
            if (f(x1)<=0.05){
            cont = false;
            System.out.println("The Program did it in "+iterations_number+" Step(s)");
            System.out.println("The root is: "+ x1);
             System.out.println("The Error is: "+(Math.abs(x1-x0)/x1)*100+"%");
            }
            }

            return x1;
        }

    public static void main(String[] args) {
         NewtonRaphson();

    }
}

输出是：

The Program did it in 1 Step(s)
The root is: 1.9001584993293807
The Error is: 5.254377500921955%

Answer 1

您的代码永远不会“到达最后一行”的原因可能是您指的是 NewtonRhapson() 方法中的 return 语句，因为它处于无限循环中。循环的每次迭代都与上一次相同。您在循环之外设置 x0，然后再也不设置它。鉴于循环中的其余值/计算都是从 x0 派生的，您会一遍又一遍地得到相同的结果。

Answer 2

public class NewtonRaphsonMethod {


          // let f be a function defined as f(x) = 3x - e^x + sin(x)

        public static double f (double x){

           // return (3*x-(Math.pow(Math.E, x))+Math.sin(x));
            return((Math.pow(x, 2))+5*x+6);
        }

        // let g be a function defined as g(x) = f'(x) = 3- e^x + cos (x)


     public static double g (double x){

           // return (3-(Math.pow(Math.E, x))+Math.cos(x));
         return(2*x+5);
        }


          public static double NewtonRaphson (){
              int iterations_number=0;
              boolean cont = true;
            double x0 , x1, Error=0;
            x0 =-1.8;
            x1=0;

            while (cont){

            x1 = x0 - (f(x0)/g(x0));
            Error = Math.abs(x1-x0);
            iterations_number++;
           // if (Error<=0.0000000005){
            if(iterations_number>100){
            cont = false;
            System.out.println("The Program did it in "+iterations_number+" Step(s)");
            System.out.println("The root is: "+ x1);
             System.out.println("The Error is: "+(Math.abs(x1-x0)/x1)*100+"%");
            }else{
                x0=x1;
            }
            }

            return x1;
        }

    public static void main(String[] args) {
         NewtonRaphson();

    }
}