jacobiMethodScript.js

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/**
 * Solves a system of linear equations using the Jacobi iterative method
 * @param {array} A - The coefficient matrix (must be square)
 * @param {array} b - The right-hand side vector
 * @param {array} x0 - Initial guess for solution vector
 * @param {number} [maxIterations=100] - Maximum number of iterations
 * @param {number} [tolerance=1e-7] - Convergence tolerance
 * @returns {object} An object containing:
 *  - solution: The solution vector
 *  - iterations: The number of iterations performed
 *  - converged: Boolean indicating whether the method converged
 */
export function jacobiMethod(A, b, x0, maxIterations = 100, tolerance = 1e-7) {
  const n = A.length; // Size of the square matrix
  let x = [...x0];    // Current solution (starts with initial guess)
  let xNew = new Array(n); // Next iteration's solution
  
  for (let iteration = 0; iteration < maxIterations; iteration++) {
    // Perform one iteration
    for (let i = 0; i < n; i++) {
      let sum = 0;
      // Calculate sum of A[i][j] * x[j] for j ≠ i
      for (let j = 0; j < n; j++) {
        if (j !== i) {
          sum += A[i][j] * x[j];
        }
      }
      // Update xNew[i] using the Jacobi formula
      xNew[i] = (b[i] - sum) / A[i][i];
    }
    
    // Check convergence
    let maxDiff = 0;
    for (let i = 0; i < n; i++) {
      maxDiff = Math.max(maxDiff, Math.abs(xNew[i] - x[i]));
    }
    
    // Update x for next iteration
    x = [...xNew];
    
    // If difference is small enough, we've converged
    if (maxDiff < tolerance) {
      return {
        solution: x,
        iterations: iteration + 1,
        converged: true
      };
    }
  }
  
  // If we reach here, we didn't converge within maxIterations
  return {
    solution: x,
    iterations: maxIterations,
    converged: false
  };
}