Evaluate students' ability to analyze and compare Jacobi, Incomplete Cholesky (IC), and SSOR preconditioners for the Conjugate Gradient method on ill-conditioned symmetric positive-definite systems. Assess understanding of spectral effects and convergence bounds, robustness to ill-conditioning and breakdowns, setup and application costs (fill-in, storage, flops), and the design and interpretation of numerical experiments to justify preconditioner choice.