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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.

 

How to calculate shortest vectors in a lattice
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by U. Dieter PDF
Math. Comp. 29 (1975), 827-833 Request permission

Abstract:

A method for calculating vectors of smallest norm in a given lattice is outlined. The norm is defined by means of a convex, compact, and symmetric subset of the given space. The main tool is the systematic use of the dual lattice. The method generalizes an algorithm presented by Coveyou and MacPherson, and improved by Knuth, for the determination of vectors of smallest Euclidean norm.
References
  • R. R. Coveyou and R. D. Macpherson, Fourier analysis of uniform random number generators, J. Assoc. Comput. Mach. 14 (1967), 100–119. MR 221727, DOI 10.1145/321371.321379
  • U. DIETER & J. H. AHRENS, Pseudo-Random Numbers, Preliminary version in preprint (430 pages), Wiley, New York. (To appear.)
  • Donald E. Knuth, The art of computer programming. Vol. 2: Seminumerical algorithms, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. MR 0286318
  • George Marsaglia, Random numbers fall mainly in the planes, Proc. Nat. Acad. Sci. U.S.A. 61 (1968), 25–28. MR 235695, DOI 10.1073/pnas.61.1.25
  • H. MINKOWSKI, Gesammelte Abhandlungen, especially Vol. I, pp. 243-260, Vol. II, pp. 3-42, Teubner-Verlag, Leipzig, 1911.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Math. Comp. 29 (1975), 827-833
  • MSC: Primary 10E20; Secondary 65K05
  • DOI: https://doi.org/10.1090/S0025-5718-1975-0379386-6
  • MathSciNet review: 0379386