Effective Approximate Factorization of Linear Partial Differential Operators

over an LPDO ring is called a factorization of the LPDO. If the product of an LPDO decomposition
differs from the original operator but the residual is negligible in a certain sense we call the
decomposition an approximate factorization. A simple example of a negligible residual is a
function bounded by a small constant within a prescribed domain. The operator is called
approximately reducible if a factorization in the latter sense exists. The talk introduces the
theory of approximate LPDO factorization over the coefficient field of rational functions
subject to a set of restrictions on the input and the output LPDOs. The presentation focuses
on the computational issues of deciding approximate reducibility and effectively computing the
factors. The approach generalizes to the case when the occurring LPDOs are allowed to contain
parameters. The results are substantiated by examples computed with a REDUCE implementation
of the methods.