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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Stochastic algorithms for self-consistent calculations of electronic structures
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by Taehee Ko and Xiantao Li HTML | PDF
Math. Comp. 92 (2023), 1693-1728 Request permission


The convergence property of a stochastic algorithm for the self-consistent field (SCF) calculations of electron structures is studied. The algorithm is formulated by rewriting the electronic charges as a trace/diagonal of a matrix function, which is subsequently expressed as a statistical average. The function is further approximated by using a Krylov subspace approximation. As a result, each SCF iteration only samples one random vector without having to compute all the orbitals. We consider the common practice of SCF iterations with damping and mixing. We prove that the iterates from a general linear mixing scheme converge in a probabilistic sense when the stochastic error has a second finite moment.
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Additional Information
  • Taehee Ko
  • Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
  • ORCID: 0000-0003-2522-0125
  • Email:
  • Xiantao Li
  • Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
  • MR Author ID: 701622
  • ORCID: 0000-0002-9760-7292
  • Email:
  • Received by editor(s): October 24, 2021
  • Received by editor(s) in revised form: May 1, 2022, October 19, 2022, and December 30, 2022
  • Published electronically: February 28, 2023
  • Additional Notes: This work was supported by NSF Grants DMS-1819011 and 1953120.
  • © Copyright 2023 American Mathematical Society
  • Journal: Math. Comp. 92 (2023), 1693-1728
  • MSC (2020): Primary 60G52, 65C40
  • DOI:
  • MathSciNet review: 4570338