Numerical prescriptions of early-time divergences of the in-in formalism
  In quantum field theory, the in and out states can be related to the full
Hamiltonian by the $i\epsilon$ prescription. A Wick rotation can further bring
the correlation functions to Euclidean spacetime where the integrals are better
defined. This setup is convenient for analytical calculations. However, for
numerical calculations, an infinitesimal $\epsilon$ or a Wick rotation of
numerical functions are difficult to implement. We propose two new numerical
methods to solve this problem, namely an Integral Basis method based on linear
regression and a Beta Regulator method based on Ces\`aro/Riesz summation.
Another class of partition-extrapolation methods previously used in
electromagnetic engineering is also introduced. We benchmark these methods with
existing methods using in-in formalism integrals, indicating advantages of
these new methods over the existing methods in computation time and accuracy.
