Integral approximation sequences

Jozsef Beck, Joel Spencer

Research output: Contribution to journalArticlepeer-review

Abstract

Let n linear forms Li on m variables be given, normalized so that all coefficients have absolute value at most unity. Let w1, ..., wm be real numbers and x1, ..., xm be integers. We say Ei= Li (w1, ..., wm)- Li (x1, ..., xm) is the error in approximating the w's by the x's with respect to form Li It is shown that given any w's there is an integral approximation of x's so that the errors Ei are small-roughly that(Formula presented.) simultaneously for all i.

Original languageEnglish (US)
Pages (from-to)88-98
Number of pages11
JournalMathematical Programming
Volume30
Issue number1
DOIs
StatePublished - Sep 1984

Keywords

  • Hadamard Matrix
  • Integral Approximation
  • Pigeonhole Principle
  • Probabilistic Method

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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