  The only known constructive factorization algorithm for linear partial
differential operators (LPDOs) is Beals-Kartashova (BK) factorization
\cite{bk2005}. One of the most interesting features of BK-factorization: at the
beginning all the first-order factors are constructed and afterwards the
factorization condition(s) should be checked. This leads to the important
application area - namely, numerical simulations which could be simplified
substantially if instead of computation with one LPDE of order $n$ we will be
able to proceed computations with $n$ LPDEs all of order 1. In numerical
simulations it is not necessary to fulfill factorization conditions exactly but
with some given accuracy, which we call approximate factorization. The idea of
the present paper is to look into the feasibility of solving problems of this
kind using quantifier elinination by cylindrical algebraic decomposition.
