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  1. class NewtonRaphsonHorner {
  2.  
  3.     // Evaluate f(x) using Horner's rule
  4.     static double f(double[] coeffs, double x) {       //ID=240242058 (MD Sakib)
  5.  
  6.         double result = coeffs[0];
  7.         for (int i = 1; i < coeffs.length; i++) {
  8.             result = result * x + coeffs[i];
  9.         }
  10.         return result;
  11.     }
  12.  
  13.     // Evaluate derivative f'(x) using Horner's rule
  14.     static double fPrime(double[] coeffs, double x) {
  15.         int n = coeffs.length - 1;
  16.         double result = coeffs[0] * n;
  17.         for (int i = 1; i < n; i++) {
  18.             result = result * x + coeffs[i] * (n - i);
  19.         }
  20.         return result;
  21.     }
  22.  
  23.     public static void main(String[] args) {
  24.         // Example polynomial: f(x) = 2x^3 + 3x - 1 => coefficients {2,0,3,-1}
  25.         double[] coeffs = {2, 0, 3, -1};
  26.         double x0 = 0.5;      // initial guess
  27.         double E = 1e-8;
  28.         double error = 1, x1 = x0;
  29.         int i = 0;
  30.  
  31.         System.out.printf("%-5s %-12s %-12s %-12s %-12s\n", "Iter", "x", "f(x)", "Error", "%Error");
  32.  
  33.         while (error >= E) {
  34.             double fx = f(coeffs, x0);
  35.             double fpx = fPrime(coeffs, x0);
  36.             x1 = x0 - fx / fpx;
  37.             error = Math.abs(x1 - x0);
  38.             double perError = (x0 == 0) ? 0 : (error / Math.abs(x1)) * 100;
  39.  
  40.             i++;
  41.             System.out.printf("%-5d %-12.8f %-12.8f %-12.8f %-12.8f\n", i, x1, fx, error, perError);
  42.  
  43.             x0 = x1;
  44.         }
  45.  
  46.         System.out.println("\nApproximate root = " + x1);
  47.         System.out.println("Total iterations = " + i);
  48.     }
  49. }
  50.  
Success #stdin #stdout 0.17s 56404KB
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Iter  x            f(x)         Error        %Error      
1     0.33333333   0.75000000   0.16666667   50.00000000 
2     0.31313131   0.07407407   0.02020202   6.45161290  
3     0.31290844   0.00079975   0.00022288   0.07122775  
4     0.31290841   0.00000009   0.00000003   0.00000831  
5     0.31290841   0.00000000   0.00000000   0.00000000  

Approximate root = 0.3129084094792334
Total iterations = 5
https://ideone.com/EncjMs
language:
Java (HotSpot 12)
created:
1 day ago
visibility:
public

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