Improvement of the fine-structure constant obtained from the electron g-2

At present the most precise value of the fine-structure constant is α(a_e) obtained from the anomalous magnetic moment of the electron, or the electron g-2. Further improvement in the theoretical calculation of α(a_e) requires reduction of both statistical and nonstatistical uncertainties in the Monte-Carlo evaluation of the α⁴ term. This paper analyzes some inconsistency of earlier results and identifies its source as a deviation of nonstatistical nature caused by round-off errors. This information enables us to greatly improve the statistical basis of the electron g-2 value to very high statistics while minimizing the uncertainty of the nonstatistical type. This work will lead to a value of α(a_e) with a relative uncertainty of less than 10 ^-9 when new measurements become available