  It was recently observed that chiral two-body interactions can be efficiently
represented using matrix factorization techniques such as the singular value
decomposition. However, the exploitation of these low-rank structures in a few-
or many-body framework is nontrivial and requires reformulations that
explicitly utilize the decomposition format. In this work, we present a general
least-square approach that is applicable to different few- and many-body
frameworks and allows for an efficient reduction to a low number of singular
values in the least-square iteration. We verify the feasibility of the
least-square approach by solving the Lippmann-Schwinger equation in factorized
form. The resulting low-rank approximations of the $T$ matrix are found to
fully capture scattering observables. Potential applications of the
least-square approach to other frameworks with the goal of employing tensor
factorization techniques are discussed.
