Matrix Decompositions for Telecom Network Reliability in South Africa: Stability Analysis and Convergence Proofs

This study explores matrix decomposition methods for assessing telecom network reliability in South Africa. An analytical approach is adopted, with a focus on deriving stability conditions for matrix decompositions used in network reliability analysis. A key finding is that the proposed method ensures stable and convergent solutions for the telecom network models under study. The theoretical framework established provides robust methods for evaluating the reliability of South African telecom networks using matrix decompositions. Recommendation includes further empirical validation to confirm stability in real-world scenarios. The analytical core is ŷₜ=F(xₜ;θ) with θ̂=argminθL(θ), and convergence is established under standard smoothness conditions.