A lag-average generalization of Euler's method for accelerating series (Q1907080)

The author introduces two generalizations of the standard Euler acceleration method, which are both based on the principle of lag-averaging. He shows that the lag-averaged schemes are greatly superior to the ordinary Euler method; also, these methods are superior to all of the trendy, nonlinear accelerations and to other linear accelerations like Richardson extrapolation. The cost of the lag-averaged methods is \(O(k)\) operations, in contrast to the \(O(k^2)\) cost of the \(\varepsilon\)-algorithm, where \(k\) is the total number of series terms fed to the accelerator.