MAXIMUM-ENTROPY APPROACH TO SERIES EXTRAPOLATION AND ANALYTIC CONTINUATION

We use information theory (the principle of maximum entropy) to develop an approach to the problem of extrapolating power series. We suggest a well-defined way to map the extrapolation problem onto a moment problem, and show that the use of additional information about the function being extrapolated (such as asymptotic behaviour for large arguments) is important to obtaining accurate extrapolations. We apply the method to the virial expansion for the classical hard sphere equation of state, the quantum harmonic oscillator with octic perturbation and the symmetric Anderson model of relevance to magnetic impurities in metals. In each case the mehtod yields excellent pointwise estimates of the function being extrapolated.