Trotter factorization While reading a paper on the simulation of an exciton in potassium chloride using effective mass path integrals, a partition function is given as so,
$Z = ∫ dr_1⟨r_1∣e^{−βH}∣r_1⟩$
in which a symmetric trotter factorization is applied to the aforementioned function to give Z in the form
$Z = 
\lim_{P→∞}∫ dr_1 ∫ dr_2⋯∫ dr_P \\
× [⟨r_1∣e^{−βV(r_1)/2P}e^{−βT/P}e^{−βV(r_2)/2P}∣r_2⟩⋯\\
× ⟨r_P∣e^{−βV(r_P)/2P}e^{−βT/P}e^{−βV(r_1)/2P}∣r_1⟩]$
which "physically corresponds to a discretization of
the (cyclic) quantum path of the particle in imaginary (or Euclidean)
time"
My Question
What is a symmetric trotter factorization?
I understand the definition is given above, however, I haven’t seen the term symmetric used when describing a trotter factorization so I’m a little confused.
Here is the link to the article if more context is needed to answer the question.
Disclaimer
I originally asked this on Chemistry.SE and was told to possibly ask it over here on mathematics. I understand this may be a little off topic for this site. Really what I am looking for is what a symmetric factorization would be.
Also, if someone could help me out with some better tags, that’d be much obliged.

It's symmetric in the sense that you are expressing $e^{-\beta H}=e^{-\beta(T+V)}$ as
$$
\lim_{P\rightarrow \infty}\left(e^{-\beta V/(2P)}e^{-\beta T/P}e^{-\beta V/(2P)}\right)^P
$$
(where the iterated operator is a symmetric operator), instead of as the simpler
$$
\lim_{P\rightarrow \infty}\left(e^{-\beta V/P}e^{-\beta T/P}\right)^P.
$$
Convergence, as $P\rightarrow \infty$, is faster in the symmetric case, so for numerical methods the symmetric form tends to be preferred.
