Assess learners' ability to evaluate numerical stability and convergence when selecting iterative solvers (Newton, quasi-Newton, Conjugate Gradient) for large-scale, ill-conditioned nonlinear systems. Topics include local vs global convergence and rates, effects of ill-conditioning, Hessian/Jacobian handling (exact, approximated, matrix-free), preconditioning, line search vs trust-region strategies, computational cost and storage trade-offs, stopping criteria, regularization, and interpreting convergence diagnostics to justify a solver choice and tuning decisions.