  Whether for fundamental studies or nuclear data evaluations, first-principle
calculations of atomic nuclei constitute the path forward. Today, performing
\textit{ab initio} calculations (a) of heavy nuclei, (b) of doubly open-shell
nuclei or (c) with a sub-percent accuracy is at the forefront of nuclear
structure theory. While combining any two of these features constitutes a major
challenge, addressing the three at the same time is currently impossible. From
a numerical standpoint, these challenges relate to the necessity to handle (i)
very large single bases and (ii) mode-6, \textit{i.e.} three-body, tensors
(iii) that must be stored repeatedly. Performing second-order many-body
perturbation theory(ies) calculations based on triaxially deformed and
superfluid reference states of doubly open-shell nuclei up to mass $A=72$, the
present work achieves a significant step forward by addressing challenge (i).
To do so, the memory and computational cost associated with the handling of
large tensors is scaled down via the use of tensor factorization techniques.
The presently used factorization format is based on a randomized singular value
decomposition that does not require the computation and storage of the very
large initial tensor. The procedure delivers an inexpensive and controllable
approximation to the original problem, as presently illustrated for
calculations that could not be performed without tensor factorization. With the
presently developed technology at hand, one can envision to perform
calculations of yet heavier doubly open-shell nuclei at sub-percent accuracy in
a foreseeable future.
