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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.

 

Analysis of the Feshbach–Schur method for the Fourier spectral discretizations of Schrödinger operators
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by Geneviève Dusson, Israel Michael Sigal and Benjamin Stamm HTML | PDF
Math. Comp. 92 (2023), 217-249 Request permission

Abstract:

In this article, we propose a new numerical method and its analysis to solve eigenvalue problems for self-adjoint Schrödinger operators, by combining the Feshbach–Schur perturbation theory with the spectral Fourier discretization. In order to analyze the method, we establish an abstract framework of Feshbach–Schur perturbation theory with minimal regularity assumptions on the potential that is then applied to the setting of the new spectral Fourier discretization method. Finally, we present some numerical results that underline the theoretical findings.
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Additional Information
  • Geneviève Dusson
  • Affiliation: Laboratoire de Mathématiques de Besançon, UMR CNRS 6623, Université Bourgogne Franche-Comté, 16 route de Gray, 25030 Besançon, France
  • ORCID: 0000-0002-7160-6064
  • Email: genevieve.dusson@math.cnrs.fr
  • Israel Michael Sigal
  • Affiliation: Department of Mathematics, University of Toronto, 40 St. George Street, Bahen Centre, Toronto, Ontario M5S 2E4, Canada
  • MR Author ID: 161895
  • ORCID: 0000-0001-7514-7056
  • Email: im.sigal@utoronto.ca
  • Benjamin Stamm
  • Affiliation: Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
  • MR Author ID: 824171
  • ORCID: 0000-0003-3375-483X
  • Email: best@ians.uni-stuttgart.de
  • Received by editor(s): August 24, 2020
  • Received by editor(s) in revised form: December 3, 2021, and April 22, 2022
  • Published electronically: September 23, 2022
  • © Copyright 2022 American Mathematical Society
  • Journal: Math. Comp. 92 (2023), 217-249
  • MSC (2020): Primary 65N25, 65N12, 65N15
  • DOI: https://doi.org/10.1090/mcom/3774
  • MathSciNet review: 4496964