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vatman

Untitled

May 8th, 2024
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C++ 1.70 KB | None | 0 0
  1. #include <cmath>
  2. #include <iostream>
  3.  
  4. void method_vr() {
  5.   double w = 1.2; // 0<w<2
  6.   int N_max = 10000;
  7.   int S = 0;
  8.   double eps = 0.0001;
  9.   double eps_max = 0;
  10.   double eps_cur = 0;
  11.   int n;
  12.   std::cout << "input n" << '\n';
  13.   std::cin >> n;
  14.   double a[n][n];
  15.   double x[n + 2];
  16.   x[0] = 0;
  17.   x[n + 1] = 0;
  18.   double b[n];
  19.   std::cout << "input a[n][n]" << '\n';
  20.   for (int i = 0; i < n; ++i) {
  21.     for (int j = 0; j < n; ++j) {
  22.       std::cin >> a[i][j];
  23.     }
  24.   }
  25.   std::cout << "input b[n]" << '\n';
  26.   for (int j = 0; j < n; ++j) {
  27.     std::cin >> b[j];
  28.   }
  29.   std::cout << "input x[n]" << '\n';
  30.   for (int j = 1; j < n + 1; ++j) {
  31.     std::cin >> x[j];
  32.   }
  33.   for (int i = 0; i < n; ++i) {
  34.     for (int j = 0; j < n; ++j) {
  35.       std::cout << a[i][j] << ' ';
  36.     }
  37.     std::cout << b[i] << '\n';
  38.   }
  39.  
  40.   double x_old;
  41.   double x_new;
  42.   bool f = false;
  43.   while (!f) {
  44.     for (int i = 1; i < n + 1; ++i) {
  45.       x_old = x[i];
  46.       x_new = (1 - w) * a[i - 1][i - 1] * x[i] + w * b[i - 1];
  47.       for (int j = 1; j < n + 1; ++j) {
  48.         if (j != i) {
  49.           x_new -= w * a[i - 1][j - 1] * x[j];
  50.         }
  51.       }
  52.       x_new /= a[i - 1][i - 1];
  53.       eps_cur = fabs(x_old - x_new);
  54.       if (i == 1) {
  55.         eps_max = eps_cur;
  56.       } else if (eps_cur > eps_max) {
  57.         eps_max = eps_cur;
  58.       }
  59.       x[i] = x_new;
  60.     }
  61.     S += 1;
  62.     if ((eps_max <= eps) || (S >= N_max)) {
  63.       f = true;
  64.       std::cout << "eps_max: " << eps_max << '\n';
  65.     }
  66.   }
  67.   for (int i = 1; i < n + 1; ++i) {
  68.     std::cout << S << ':' << x[i] << ' ';
  69.   }
  70.   std::cout << '\n';
  71.   std::cout << "count of steps: " << S << '\n';
  72. }
  73.  
  74. int main() {
  75.   method_vr();
  76.   return 0;
  77. }
  78.  
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