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.


Structured data-sparse approximation to high order tensors arising from the deterministic Boltzmann equation
HTML articles powered by AMS MathViewer

by Boris N. Khoromskij PDF
Math. Comp. 76 (2007), 1291-1315 Request permission


We develop efficient data-sparse representations to a class of high order tensors via a block many-fold Kronecker product decomposition. Such a decomposition is based on low separation-rank approximations of the corresponding multivariate generating function. We combine the $Sinc$ interpolation and a quadrature-based approximation with hierarchically organised block tensor-product formats. Different matrix and tensor operations in the generalised Kronecker tensor-product format including the Hadamard-type product can be implemented with the low cost. An application to the collision integral from the deterministic Boltzmann equation leads to an asymptotical cost $O(n^4\log ^\beta n)$ - $O(n^5\log ^\beta n)$ in the one-dimensional problem size $n$ (depending on the model kernel function), which noticeably improves the complexity $O(n^6\log ^\beta n)$ of the full matrix representation.
Similar Articles
Additional Information
  • Boris N. Khoromskij
  • Affiliation: Max-Planck-Institute for Mathematics in the Sciences, Inselstr. 22-26, D-04103 Leipzig, Germany
  • Email:
  • Received by editor(s): February 22, 2005
  • Received by editor(s) in revised form: October 4, 2005
  • Published electronically: February 16, 2007
  • © Copyright 2007 American Mathematical Society
  • Journal: Math. Comp. 76 (2007), 1291-1315
  • MSC (2000): Primary 65F50, 65F30; Secondary 15A24, 15A99
  • DOI:
  • MathSciNet review: 2299775