Algorithm for Proportional Matrices in Reals and Integers

Michel Balinski and Gabrielle Demange

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Abstract: Let R be the set of nonnegative matrices whose row and column sums fall between specific limits and whose entries sum to some fixed h > 0. Closely related axiomatic approaches have been developed to ascribe meanings to the statements: the real matrix fe R and the integer matrix a ~ R are "proportional to" a given matrix p ~> 0. These approaches are described, conditions under which proportional solutions exist are characterized, and algorithms are given for finding proportional solutions in each case.

Keywords: algorithm; proportional matrices (search for similar items in EconPapers)
Date: 1989
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00585327
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Published in Mathematical Programming, Series A, 1989, 45 (1-3), pp.193-210. ⟨10.1007/BF01589103⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-00585327

DOI: 10.1007/BF01589103

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