Integral approximation sequences

Jozsef Beck; Joel Spencer

doi:10.1007/BF02591800

Integral approximation sequences

Jozsef Beck, Joel Spencer

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English (US)
Pages (from-to)	88-98
Number of pages	11
Journal	Mathematical Programming
Volume	30
Issue number	1
DOIs	https://doi.org/10.1007/BF02591800
State	Published - Sep 1984

Keywords

Hadamard Matrix
Integral Approximation
Pigeonhole Principle
Probabilistic Method

ASJC Scopus subject areas

Software
General Mathematics

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10.1007/BF02591800

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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.",

keywords = "Hadamard Matrix, Integral Approximation, Pigeonhole Principle, Probabilistic Method",

author = "Jozsef Beck and Joel Spencer",

year = "1984",

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doi = "10.1007/BF02591800",

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AB - 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.

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KW - Integral Approximation

KW - Pigeonhole Principle

KW - Probabilistic Method

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Integral approximation sequences

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Keywords

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