Test candidates' ability to evaluate numerical stability, convergence behavior, and computational trade-offs of iterative solvers (Conjugate Gradient, GMRES, BiCGSTAB) for large sparse linear systems. Assess understanding of spectral influences on convergence, residual/error norms, breakdowns and stagnation, memory and FLOP costs, preconditioner selection and effect, GMRES restart strategies, and solver choice criteria for symmetric positive-definite versus nonsymmetric problems. Include interpretation of solver diagnostics and recommendation of methods under competing demands of robustness, precision, and runtime for real-world sparse matrices.