In this article, we study the accuracy and reproducibility issues in EigenExa due to the non-associative of floating-point operations, rounding-off errors, dynamic thread scheduling, and different reduction trees, etc. By investigating the EigenExa’s algorithmic structure and the corresponding implementation, we find the origins of the non-reproducibility and demonstrate it on the numerical results. As a solution, we, at first, propose to apply the accurate and reproducible parallel reduction from the ExBLAS library. Moreover, we outline possible extensions to ExBLAS that would enhance further the numerical properties of EigenExa.