Gaussian Elimination (Gauss Eliminasyonu) Algoritması

1function gaussianElimination(matrix: number[][], results: number[]): number[] {
2  const n = matrix.length;
3  const aug: number[][] = matrix.map((row, i) => [...row, results[i]]);
4  for (let i = 0; i < n; i++) {
5    let maxRow = i;
6    for (let k = i + 1; k < n; k++) { if (Math.abs(aug[k][i]) > Math.abs(aug[maxRow][i])) { maxRow = k; } }
7    const temp = aug[i]; aug[i] = aug[maxRow]; aug[maxRow] = temp;
8    if (Math.abs(aug[i][i]) < 1e-9) { throw new Error('Matris tekildir veya sonsuz çözümlüdür.'); }
9    for (let k = i + 1; k < n; k++) {
10      const factor = aug[k][i] / aug[i][i];
11      for (let j = i; j <= n; j++) { aug[k][j] -= factor * aug[i][j]; }
12    }
13  }
14  const x = Array(n).fill(0);
15  for (let i = n - 1; i >= 0; i--) {
16    let sum = 0;
17    for (let j = i + 1; j < n; j++) { sum += aug[i][j] * x[j]; }
18    x[i] = (aug[i][n] - sum) / aug[i][i];
19  }
20  return x;
21}