Solve systems of linear equations efficiently with our SOR Method Calculator. This powerful tool applies the Successive Over-Relaxation iterative technique, an advanced version of Gauss-Seidel, to find approximate solutions rapidly. Ideal for numerical analysis and computational mathematics.
Formula:
The Successive Over-Relaxation (SOR) method updates each variable iteratively using the formula:xi(k+1) = (1 - ω)xi(k) + ω * (1 / aii) * (bi - ∑j=1i-1 aijxj(k+1) - ∑j=i+1n aijxj(k))
Where:
xi(k+1): The new approximation for the i-th variable at iteration k+1.xi(k): The previous approximation for the i-th variable at iteration k.ω(omega): The relaxation parameter, a value between 0 and 2 (0 < ω < 2) that controls the speed of convergence.aij: The coefficient of xj in the i-th equation of the system Ax = b.bi: The constant term in the i-th equation.n: The total number of equations/variables in the system.