java java中的二分法实现

Bisection method implementation in java

提问by tofu

I am implementing the bisection method for solving equations in java. I had initially coded the solution for a pre-defined polynomial equation x^3 + 4x^2 - 10. Now I am generalizing the solution for any polynomial which the user inputs.

我正在实现用于在 Java 中求解方程的二分法。我最初为预定义的多项式方程 x^3 + 4x^2 - 10 编写了解决方案。现在我正在推广用户输入的任何多项式的解决方案。

I read the coefficients of corresponding degrees. Now I only need to tweak the f() method so that I can evaluate the f(a) , f(b) and f(c) .

我读了相应度数的系数。现在我只需要调整 f() 方法，以便我可以评估 f(a) 、 f(b) 和 f(c) 。

// BISECTION METHOD IMPLEMENTATION IN JAVA
// This program uses bisection method to solve for x^3 + 4x^2 -10 = 0

package nisarg;
import java.util.Scanner;

public class BetterBisection {

   public static void main(String[] args) {
      double a, b, c; // a, b and c have the usual meaning
      double f_of_a, f_of_b; // f_of_a, f_of_b store values of f(a) and f(b)
                             // respectively
      int highest_degree;
      System.out.println("What is the highest degree of your polynomial? ");
      Scanner input = new Scanner(System.in);
      highest_degree = input.nextInt();
      for (int i = highest_degree; i >= 0; i--) {
         int coeff_deg_i;
         coeff_deg_i = poly_input(i);
         // System.out.println(coeff_deg_i);
      }
      // The following do-while loop keeps asking the user for a and b until
      // f(a)f(b) does not become negative
      do {
         a = input();
         b = input();
         if (f(a) * f(b) >= 0) {
            System.out
                  .println("Sorry the two numbers are not bracketing the root.  Please try again ");
         }
      } while (f(a) * f(b) >= 0);
      f_of_a = f(a);
      f_of_b = f(b);
      double root = bisectionMethod(f_of_a, f_of_b, a, b);
      System.out.println("Root is : " + root);
   }

   public static double input() { // Reads in the bracketing number i.e a and b
      Scanner input = new Scanner(System.in);
      System.out.println("Enter a bracketing number");
      return (input.nextDouble());
   }

   public static double f(double num) { // Calculates f(x) given x and returns
                                        // f(x)
      final int COEFF_DEG_3 = 1; // Coefficient of x^3
      final int COEFF_DEG_2 = 4; // Coefficient of x^2
      final int COEFF_DEG_0 = -10; // Coefficient of x^0
      return (COEFF_DEG_3 * Math.pow(num, 3) + COEFF_DEG_2 * Math.pow(num, 2) + COEFF_DEG_0
            * Math.pow(num, 0));
   }

   public static double bisectionMethod(double f_of_a, double f_of_b, double a,
         double b) { // Does the actual work of evaluating
      double c; // the root using the method of bisection.
      double f_of_c;
      final double TOLERANCE = 0.0001;
      while (Math.abs(a - b) > TOLERANCE) {
         c = (a + b) / 2;
         f_of_c = f(c);
         if (f_of_c * f(a) == 0 || f_of_c * f(b) == 0) {
            return c;
         } else if (f_of_c * f(a) > 0) {
            a = c;
         } else {
            b = c;
         }
      }
      return (a + b) / 2;
   }

   public static int poly_input(int degree) {
      System.out.println("Please enter coefficient for degree " + degree);
      Scanner input = new Scanner(System.in);
      int coefficient;
      coefficient = input.nextInt();
      return coefficient;
   }
}

回答by Mureinik

You can't use loops to define variables. Either have 12 explicit variables:

您不能使用循环来定义变量。要么有 12 个显式变量：

public class global {
    public static int coeff_deg_1;
    public static int coeff_deg_2;
    public static int coeff_deg_3;
    // and so on...
}

Or define a single array with 12 elements:

或者定义一个包含 12 个元素的数组：

public class global {
    public static final int coeff_degs = new int[12];
}

回答by Tu?bars Hepta?k?n

here is a recursive one:

这是一个递归的：

public static double f(double x) {
            return (x*x*x)-4*x-10;
}
public static double RecursiveBisection(Function fct, final double left, final double right, final double tolerance) {
    double x = 0;
    double dx = 0;
    if ( Math.abs(right - left) < tolerance ) // base case
        return (left + right) / 2;
    else { // recursive case
        x = (left + right)/2;
        System.out.println("Root obtained: " + x);
        dx = right - left;
        System.out.println("Estimated error: " + dx);
        if ( fct.f(left) * fct.f(x) > 0 ) // on same side
            return RecursiveBisection (fct, x, right, tolerance);
        else // opposite side
            return RecursiveBisection(fct, left, x, tolerance);

    }
}