  We study the maximum entropy (MaxEnt) approach for analytical continuation of
spectral data from imaginary times to real frequencies. The total error is
divided in a statistical error, due to the noise in the input data, and a
systematic error, due to deviations of the default function, used in the MaxEnt
approach, from the exact spectrum. We find that the MaxEnt approach in its
classical formulation can lead to a nonoptimal balance between the two types of
errors, leading to an unnecessary large statistical error. The statistical
error can be reduced by splitting up the data in several batches, performing a
MaxEnt calculation for each batch and averaging. This can outweigh an increase
in the systematic error resulting from this approach. The output from the
MaxEnt result can be used as a default function for a new MaxEnt calculation.
Such iterations often lead to worse results due to an increase in the
statistical error. By splitting up the data in batches, the statistical error
is reduced and and the increase resulting from iterations can be outweighed by
a decrease in the systematic error. Finally we consider a linearized version to
obtain a better understanding of the method.
