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  1. #include <iostream>
  2. #include <iomanip>
  3. #include <cmath>
  4. #include <string>
  5.  
  6. using namespace std;
  7.  
  8. double function(double x) {
  9.     return x * x - 34.0;
  10. }
  11.  
  12. void secant_method(double x1, double x2, double tolerance) {
  13.     double f1 = function(x1);
  14.     double f2 = function(x2);
  15.     double x3;
  16.     int iteration = 0;
  17.  
  18.     cout << setprecision(6) << fixed;
  19.  
  20.     cout << "--- Secant Method for f(x) = x^2 - 34 ---" << endl;
  21.     cout << "Initial Guesses (x1, x2): (" << x1 << ", " << x2 << ")" << endl;
  22.     cout << "Tolerance (E): " << scientific << tolerance << fixed << endl;
  23.     cout << "\n";
  24.  
  25.     cout << setw(10) << "Iter"
  26.          << setw(15) << "x1"
  27.          << setw(15) << "x2"
  28.          << setw(15) << "x3"
  29.          << setw(15) << "f(x1)"
  30.          << setw(15) << "f(x2)"
  31.          << setw(15) << "f(x3)" << endl;
  32.     cout << string(95, '-') << endl;
  33.  
  34.     while (abs(function(x2)) >= tolerance && iteration < 50) {
  35.         iteration++;
  36.  
  37.         if (abs(f2 - f1) < 1e-8) {
  38.             cout << "Error: Denominator near zero. Secant line is almost horizontal." << endl;
  39.             break;
  40.         }
  41.  
  42.         x3 = x2 - (f2 * (x2 - x1)) / (f2 - f1);
  43.         double f3 = function(x3);
  44.  
  45.         cout << setw(10) << iteration
  46.              << setw(15) << x1
  47.              << setw(15) << x2
  48.              << setw(15) << x3
  49.              << setw(15) << f1
  50.              << setw(15) << f2
  51.              << setw(15) << f3 << endl;
  52.  
  53.         x1 = x2;
  54.         f1 = f2;
  55.         x2 = x3;
  56.         f2 = f3;
  57.  
  58.         if (abs(f3) < tolerance) {
  59.             break;
  60.         }
  61.     }
  62.  
  63.     cout << string(95, '-') << endl;
  64.     cout << "The final root is approximately: " << x2 << endl;
  65.     cout << "Found after " << iteration << " iterations." << endl;
  66. }
  67.  
  68. int main() {
  69.     double x1_initial = 4.0;
  70.     double x2_initial = 2.0;
  71.     double tolerance = 0.000001;
  72.  
  73.     secant_method(x1_initial, x2_initial, tolerance);
  74.  
  75.     return 0;
  76. }
Success #stdin #stdout 0s 5308KB
comments (?)
stdin 
Standard input is empty
stdout 
--- Secant Method for f(x) = x^2 - 34 ---
Initial Guesses (x1, x2): (4.000000, 2.000000)
Tolerance (E): 1.000000e-06

      Iter             x1             x2             x3          f(x1)          f(x2)          f(x3)
-----------------------------------------------------------------------------------------------
         1       4.000000       2.000000       7.000000     -18.000000     -30.000000      15.000000
         2       2.000000       7.000000       5.333333     -30.000000      15.000000      -5.555556
         3       7.000000       5.333333       5.783784      15.000000      -5.555556      -0.547845
         4       5.333333       5.783784       5.833063      -5.555556      -0.547845       0.024626
         5       5.783784       5.833063       5.830943      -0.547845       0.024626      -0.000100
         6       5.833063       5.830943       5.830952       0.024626      -0.000100      -0.000000
-----------------------------------------------------------------------------------------------
The final root is approximately: 5.830952
Found after 6 iterations.
https://ideone.com/qWsAZg
language:
C++ (gcc 8.3)
created:
4 hours ago
visibility:
public

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