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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.


A fast algorithm for the energy space boson Boltzmann collision operator
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by Jingwei Hu and Lexing Ying PDF
Math. Comp. 84 (2015), 271-288 Request permission


This paper introduces a fast algorithm for the energy space boson Boltzmann collision operator. Compared to the direct $O(N^3)$ calculation and the previous $O(N^2\log N)$ method [Markowich and Pareschi, 2005], the new algorithm runs in complexity $O(N\log ^2N)$, which is optimal up to a logarithmic factor ($N$ is the number of grid points in energy space). The basic idea is to partition the 3-D summation domain recursively into elementary shapes so that the summation within each shape becomes a special double convolution that can be computed efficiently by the fast Fourier transform. Numerical examples are presented to illustrate the efficiency and accuracy of the proposed algorithm.
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Additional Information
  • Jingwei Hu
  • Affiliation: Institute for Computational Engineering and Sciences (ICES), The University of Texas at Austin, 1 University Station, C0200, Austin, Texas 78712
  • Email:
  • Lexing Ying
  • Affiliation: Department of Mathematics and Institute for Computational and Mathematical Engineering (ICME), Stanford University, 450 Serra Mall, Bldg 380, Stanford, California 94305
  • Email:
  • Received by editor(s): June 2, 2012
  • Received by editor(s) in revised form: December 12, 2012, and December 27, 2012
  • Published electronically: March 21, 2014
  • Additional Notes: The first author was supported by an ICES Postdoctoral Fellowship
    The second author was partially supported by NSF under CAREER award DMS-0846501
  • © Copyright 2014 American Mathematical Society
  • Journal: Math. Comp. 84 (2015), 271-288
  • MSC (2010): Primary 35Q20, 82C10, 65D32, 44A35, 65T50
  • DOI:
  • MathSciNet review: 3266960