Assess students' ability to analyze convergence behavior and error propagation of the conjugate gradient (CG) method for symmetric positive-definite systems. Scope includes derivation and use of A‑norm error bounds, dependence of convergence on the eigenvalue distribution and condition number (e.g., Chebyshev polynomial bounds), finite‑arithmetic finite‑termination vs. exact arithmetic, effects of preconditioning and eigenvalue clustering, and the impact of floating‑point roundoff (loss of conjugacy, residual stagnation). Tasks should combine theoretical derivations, interpretation of convergence bounds, and short numerical examples that illustrate spectral effects and mitigation strategies (reorthogonalization, residual recomputation, restarts).