Cross approximation in tensor electron density computations

I. V. Oseledets, D. V. Savostyanov, E. E. Tyrtyshnikov

Research output: Contribution to journalArticle

Abstract

We propose new tensor approximation algorithms for certain discrete functions related with Hartree-Fock/Kohn-Sham equations. Given a canonical tensor representation for the electron density function (for example, produced by quantum chemistry packages such as MOLPRO), we obtain its Tucker approximation with much fewer parameters than the input data and the Tucker approximation for the cubic root of this function, which is part of the Kohn-Sham exchange operator. The key idea is in the fast and accurate prefiltering of possibly large-scale factors of the canonical tensor input. The new algorithms are based on the incomplete cross approximation method applied to matrices and tensors of order 3 and outperform other tools for the same purpose.First, we show that the cross approximation method is robust and much faster than the singular value decomposition-based approach. As a consequence, it becomes possible to increase the resolution of grid and the complexity of molecules that can be handled by the Hartree-Fock chemical models. Second, we propose a new fast approximation method for f1/3(x, y, z), based on the factor prefiltering method for f(x, y, z) and certain mimic approximation hypothesis. Third, we conclude that the Tucker format has advantages in the storage and computation time compared with the ubiquitous canonical format.

Original languageEnglish
Pages (from-to)935-952
Number of pages18
JournalNumerical Linear Algebra with Applications
Volume17
Issue number6
DOIs
Publication statusPublished - 1 Dec 2010

Keywords

  • Canonical decomposition
  • Cross approximation
  • Electron density
  • Hartree-Fock/Kohn-Sham
  • Tucker approximation

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    Oseledets, I. V., Savostyanov, D. V., & Tyrtyshnikov, E. E. (2010). Cross approximation in tensor electron density computations. Numerical Linear Algebra with Applications, 17(6), 935-952. https://doi.org/10.1002/nla.682