Enhanced optimization of high order concentrated matrix-exponential distributions
Salah Al-Deen Almousa, Miklós Telek · Az Eszterházy Károly Tanárképző Főiskola tudományos közleményei. Tanulmányok a matematikai tudományok köréből/Az Eszterházy Károly Főiskola tudományos közleményei. Tanulmányok a matematikai tudományok köréből/Annales mathematicae et informaticae · 2021
This paper presents numerical methods for finding high order concentrated matrix-exponential (ME) distributions, whose squared coefficient of variation (SCV) is very low.Due to the absence of symbolic construction to obtain the most concentrated ME distributions, non-linear optimization problems are defined to obtain high order concentrated matrix-exponential (CME) distributions .The number of parameters to optimize increases with the order in the "full" version of the optimization problem.For orders, where "full" optimization is infeasible (𝑛 > 184), a "heuristic" optimization procedure, optimizing only 3 parameters independent of the order, was proposed in [6].In this work we present an enhanced version of this heuristic optimization procedure, optimizing only 6 parameters independent of the order, which results in CME distributions with lower SCV than the existing 3-parameter method.The SCV gain of the new procedure compared to the old one is * This work is partially supported by the OTKA K-123914 and the NKFIH BME NC TKP2020 projects.