Gauss–Seidel Iteration
See how using each freshly updated coordinate changes an iterative linear solve and its convergence.
Free theory articleSee how using each freshly updated coordinate changes an iterative linear solve and its convergence.
Concept & interpretation
The Gauss–Seidel method is an iterative technique for solving a square system of linear equations of the form Ax = b. Unlike the Jacobi method, which uses the values from the previous iteration to compute all updates for the current iteration, the Gauss–Seidel method uses the newly updated values as soon as they are available.
Interactive Experiment
You can try out this method yourself in the Gauss–Seidel Iteration module.
- Change the Coupling c to see how the off-diagonal entries affect the spectral radius and convergence.
- Adjust b1 and b2 to change the target vector b.
- Modify the Initial x and Initial y to start the iteration from different points in the plane.
- Increase the number of Sweeps to trace the sequence of iterates and observe how they approach the exact solution or diverge.