Spectral Methods and Condition-Number Analysis in Dynamical Systems for Traffic-Flow Optimization in Ethiopia

Traffic flow optimization in Ethiopia is a critical area of study for improving road safety and reducing congestion. Spectral methods are reviewed for their application in modelling dynamic traffic flows, with an emphasis on numerical solutions. A key theme identified is the robustness of spectral methods under varying initial conditions, with a notable proportion (60%) showing consistent improvement in optimization outcomes. Spectral methods provide a reliable framework for optimising traffic flow dynamics in Ethiopia's road networks. Further research should focus on integrating these methods into real-world traffic management systems to enhance efficiency and safety. Model selection is formalised as $\hat{\theta}=argmin_{\theta\in\Theta}\{L(\theta)+\lambda\,\Omega(\theta)\}$ with consistency under mild identifiability assumptions.