[Assess students' ability to analyze convergence behavior, stability, and error estimates for Jacobi, Gauss–Seidel, SOR, and Conjugate Gradient methods applied to large sparse linear systems; include derivation and interpretation of convergence criteria (spectral radius, eigenvalue bounds, A‑norm estimates), optimal relaxation for SOR, CG convergence in Krylov subspaces and dependence on condition number, effects of preconditioning, finite‑precision and rounding error propagation, practical stopping criteria, and computational cost/scalability considerations for sparse matrices.]