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Bibliographic Details
Main Authors: Pierce, Karl, Rishi, Varun, Valeev, Edward F.
Format: Preprint
Published: 2020
Subjects:
Online Access:https://arxiv.org/abs/2012.13002
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Table of Contents:
  • Approximation of a tensor network by approximating (e.g., factorizing) one or more of its constituent tensors can be improved by canceling the leading-order error due to the constituents' approximation. The utility of such robust approximation is demonstrated for robust canonical polyadic (CP) approximation of a (density-fitting) factorized 2-particle Coulomb interaction tensor. The resulting algebraic (grid-free) approximation for the Coulomb tensor, closely related to the factorization appearing in pseudospectral and tensor hypercontraction approaches, is efficient and accurate, with significantly reduced rank compared to the naive (non-robust) approximation. Application of the robust approximation to the particle-particle ladder term in the coupled-cluster singles and doubles reduces the size complexity from $\mathcal{O}(N^6)$ to $\mathcal{O}(N^5)$ with robustness ensuring negligible errors in chemically-relevant energy differences using CP ranks approximately equal to the size of the density-fitting basis.