https://doi.org/10.1140/epjs/s11734-023-00928-z
Regular Article
On the sum-of-products to product-of-sums transformation between analytical low-rank approximations in finite basis representation
1
Faculty of Chemistry and Food Chemistry, Technische Universität Dresden, 01069, Dresden, Germany
2
CNRS, Institut des Sciences Moléculaires d’Orsay, Université Paris-Saclay, 91405, Orsay, France
a
ramon_lorenzo.panades-barrueta@tu-dresden.de
d
daniel.pelaez-ruiz@universite-paris-saclay.fr
Received:
19
January
2023
Accepted:
2
July
2023
Published online:
16
August
2023
In this work, we analyze and compare different possible strategies for the transformations among low-rank (i.e., few number of terms) tensor approximations. The motivation behind this is to achieve compact yet accurate representations of potential-like operators (scalar fields) in symbolic or analytical form. We do this analysis from a formal and from a numerical perspective. Specifically, we concentrate on Tucker and Canonic Polyadic ansätze. We introduce the sum-of-product finite basis representations (SOP-FBR) for both. Here, the factor matrices (aka single-particle functions) are approximated through a set of auxiliary basis functions, specific to the system. In this way, analytical, grid-independent, low-rank expressions can be obtained. We illustrate how finite-precision arithmetic hinders transformations among all these forms. The solution to this issue seems to adapt current algorithms to high-precision arithmetic at the expense of an increase in CPU times.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
