Matrix approximation and Tusnády's problem

  • Authors:
  • Benjamin Doerr

  • Affiliations:
  • Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123 Saarbrücken, Germany

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2007

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Abstract

We consider the problem of approximating a given matrix by an integer one such that in all geometric submatrices the sum of the entries does not change by much. We show that for all integers m,n=2 and real matrices A@?R^m^x^n there is an integer matrix B@?Z^m^x^n such that |@?i@?I@?j@?J(a"i"j-b"i"j)|