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omega = constant_omega This is only possible if all ( \omega_i ) are equal. If not, MSOR and SOR are different iterative methods . No exact equivalence exists unless you reorder the system or change the splitting.
[ x_i^(k+1) = (1 - \omega) x_i^(k) + \frac\omegaa_ii \left( b_i - \sum_j < i a_ij x_j^(k+1) - \sum_j > i a_ij x_j^(k) \right) ]
Set all ( \omega_i ) in your code to this single ( \omega ). The algorithm becomes: [ x_i^(k+1) = (1 - \omega) x_i^(k) + \frac\omegaa_ii \left( b_i - \sum_j < i a_ij x_j^(k+1) - \sum_j > i a_ij x_j^(k) \right) ] convert msor to sor
In the world of numerical linear algebra, iterative methods are essential for solving large, sparse systems of linear equations, ( Ax = b ). Among the most famous classical iterative techniques are the Jacobi, Gauss-Seidel, and Successive Over-Relaxation (SOR) methods.
From MSOR to SOR: Simplifying the Modified Successive Over-Relaxation Method omega = constant_omega This is only possible if
if i % 2 == 0: omega = omega_even else: omega = omega_odd Convert to:
for i in range(n): if i < n/2: w = 1.2 else: w = 1.8 x_new[i] = (1-w)*x_old[i] + w*(b[i] - sum(A[i][j]*x_new[j] for j<i) - sum(A[i][j]*x_old[j] for j>i)) / A[i][i] [ x_i^(k+1) = (1 - \omega) x_i^(k) +
MSOR often has logic like: