Skip to Main Content

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.


Robust BPX preconditioner for fractional Laplacians on bounded Lipschitz domains
HTML articles powered by AMS MathViewer

by Juan Pablo Borthagaray, Ricardo H. Nochetto, Shuonan Wu and Jinchao Xu
Math. Comp. 92 (2023), 2439-2473
Published electronically: June 9, 2023


We propose and analyze a robust Bramble-Pasciak-Xu (BPX) preconditioner for the integral fractional Laplacian of order $s\in (0,1)$ on bounded Lipschitz domains. Compared with the standard BPX preconditioner, an additional scaling factor $1-\widetilde {\gamma }^s$, for some fixed $\widetilde {\gamma } \in (0,1)$, is incorporated to the coarse levels. For either quasi-uniform grids or graded bisection grids, we show that the condition numbers of the resulting systems remain uniformly bounded with respect to both the number of levels and the fractional power.
Similar Articles
Bibliographic Information
  • Juan Pablo Borthagaray
  • Affiliation: Departamento de Matemática y Estadística del Litoral, Universidad de la República, Salto, Uruguay
  • Address at time of publication: Instituto de Matemática y Estadística Rafael Laguardia, Universidad de la República, Montevideo, Uruguay
  • MR Author ID: 1171838
  • ORCID: 0000-0001-5535-4939
  • Email:
  • Ricardo H. Nochetto
  • Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742; and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742
  • MR Author ID: 131850
  • ORCID: 0000-0002-6678-6857
  • Email:
  • Shuonan Wu
  • Affiliation: School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
  • MR Author ID: 1021082
  • ORCID: 0000-0003-0578-4097
  • Email:
  • Jinchao Xu
  • Affiliation: Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802
  • MR Author ID: 228866
  • Email:
  • Received by editor(s): June 2, 2021
  • Received by editor(s) in revised form: July 15, 2022, December 28, 2022, and March 7, 2023
  • Published electronically: June 9, 2023
  • Additional Notes: The first author was supported in part by NSF grant DMS-1411808 and Fondo Vaz Ferreira grant 2019-068. The second author was supported in part by NSF grant DMS-1411808. The third author was supported in part by the National Natural Science Foundation of China grant No. 12222101 and No. 11901016. The fourth author was supported in part by NSF grant DMS-1819157
  • © Copyright 2023 American Mathematical Society
  • Journal: Math. Comp. 92 (2023), 2439-2473
  • MSC (2020): Primary 65F08, 65N30, 65M50, 35R11
  • DOI: