Integral approximation sequences |
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Authors: | Jozsef Beck Joel Spencer |
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Institution: | (1) Mathematical Institute, Budapest, Hungary;(2) Mathematical Department SUNY at Stony Brook, Stony Brook, NY, USA |
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Abstract: | Letn linear formsL
i
onm variables be given, normalized so that all coefficients have absolute value at most unity. Letw
1, ...,w
m
be real numbers andx
1, ...,x
m
be integers. We sayE
i
=L
i
(w
1, ...,w
m
)-L
i
(x
1, ...,x
m
) is the error in approximating thew's by thex's with respect to formL
i
It is shown that given anyw's there is an integral approximation ofx's so that the errorsE
i
are small-roughly that
simultaneously for alli. |
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Keywords: | Integral Approximation Hadamard Matrix Probabilistic Method Pigeonhole Principle |
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