Archimedian Double Mean Process
We can view double mean as a general process to find means of two input numbers using as a recurrence formula of two means.
Compare this difference equation formula with Gaussian Double mean process .
The Archimedean double mean process has a very nice property that the sequence and will converge to a common limit with linear convergence rate. However, the common limit is not necessarily produce means. For example, if we use arithmetic and geometric mean respectively, we will get which is not means or average.
We use harmonic mean and geometric mean
Then the sequence and will converge to a common limit
Notice that this Archimedean harmonic-geometric mean is not symmetric mean, because in general, .
Preferable reference for this tutorial is
Teknomo, Kardi (2015) Mean and Average. https:\\people.revoledu.com\kardi\tutorial\BasicMath\Average\