Water-resource allocation in Rwanda faces complex optimization challenges due to varying water availability across different regions and sectors. Spectral methods were applied using eigenvalue analysis to optimise allocation strategies. A condition-number analysis was conducted to assess the sensitivity of solutions to perturbations. Eigenvalues indicated significant variations in system stability across regions, with some areas requiring higher precision for optimal allocation. The spectral and condition-number analyses provided insights into water resource distribution efficiency. Further empirical studies are recommended to validate findings and inform policy decisions. Optimization, Numerical Methods, Water Resources, Condition Number, Stability Analysis Model selection is formalised as $\hat{\theta}=argmin_{\theta\in\Theta}\{L(\theta)+\lambda\,\Omega(\theta)\}$ with consistency under mild identifiability assumptions.