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  1. //0JvQtdGJ0LXQvdC60L4=
  2. #include <iostream>
  3. #include <math.h>
  4. #include <iomanip>
  5.  
  6. using namespace std;
  7.  
  8. double eps = 0.0001;
  9.  
  10. double f(const double x) {
  11.     return log(2 * x) - 9 * x + 4;
  12. }
  13. double PodilVidrizkaNaDva(double p, double q){
  14. 	double a{};
  15.     while (fabs(p - q) >= eps) {
  16.         a = (p + q) / 2;
  17.  
  18.         if (f(p) * f(a) < 0)
  19.             q = a;
  20.  
  21.         else
  22.             p = a;
  23.     }
  24.     return a;
  25. }
  26. double ProstyhIteracyyFormula(const double x) {
  27.     // log2x = 9x - 4
  28.     // => x = (log2x + 4) / 9
  29.     return (log(2 * x) + 4) / 9;
  30. }
  31.  
  32. double NewtonFormula(const double x) {
  33.     // x n+1 = x - f(xn)/f`(xn)
  34.     return x - f(x) / (1 / (2 * x) - 9);
  35. }
  36.  
  37. double Iterations(double(*f)(double x), const double a) {
  38.     if (fabs(f(a) - f(f(a))) <= eps)
  39.         return f(a);
  40.     return Iterations(f, f(a));
  41. }
  42.  
  43. double MethodHordFormula(const double a, const double b) {
  44.     return b - (f(b) * (b - a) / (f(b) - f(a)));
  45. }
  46. double Iterations(const double a, const double b) {
  47.  
  48.     if (fabs(MethodHordFormula(a,b) - MethodHordFormula(b, MethodHordFormula(a,b))) <= eps)
  49.         return MethodHordFormula(a,b);
  50.  
  51.     return Iterations(MethodHordFormula(a,b), MethodHordFormula(b, MethodHordFormula(a, b)));
  52. }
  53. int main()
  54. {
  55.     cout << setprecision(10);
  56.     cout << "metod podilu navpil\t-> "<< PodilVidrizkaNaDva(0.1,1)<< endl;
  57.     cout << "metod hord\t-> " << Iterations(0.1, 0.5) << endl;
  58.     cout << "metod prostyh iteracy\t-> " << Iterations(ProstyhIteracyyFormula, 0.1) << endl;
  59. 	cout << "Newton method\t-> " << Iterations(NewtonFormula, 0.1) << endl;
  60.     return 0;
  61. }
Success #stdin #stdout 0.01s 5292KB
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metod podilu navpil	-> 0.4268981934
metod hord	-> 0.4268853061
metod prostyh iteracy	-> 0.4268074023
Newton method	-> 0.4268986886
https://ideone.com/pMVq0q
language:
C++ (gcc 8.3)
created:
20 hours ago
visibility:
public

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