Comparative numerical laboratory
Iterative Linear Solvers: Jacobi, Gauss--Seidel, SOR — Chapter 5
Solve the same diagonally dominant system and compare residual decay.
\[
4x+y=1, x+3y=2.
\]
Methods compared
| Method | Convenience | Inconvenience / warning |
|---|---|---|
| Jacobi | Parallel and simple. | Often slow. |
| Gauss--Seidel | Usually faster than Jacobi. | Sequential dependence; ordering matters. |
| SOR | Can accelerate Gauss--Seidel. | Sensitive to \(\omega\); bad choices can diverge. |
Illustrative plot / animation
Numerical diagnostics
What the student must compare
- residual norm
- iteration matrix behavior
- sensitivity to relaxation
- stopping tolerance