Algorithm for Proportional Matrices in Reals and Integers

Michel L. Balinski (1) , Gabrielle Demange (2)

1 X-DEP-ECO - Département d'Économie de l'École Polytechnique
2 CECO - Laboratoire d'économétrie de l'École polytechnique

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.

Mots clés: algorithm; proportional matrices

Domaines: Economies et finances

Michel L. Balinski, Gabrielle Demange. Algorithm for Proportional Matrices in Reals and Integers. Mathematical Programming, Series A, 1989, 45 (1-3), pp.193-210. ⟨10.1007/BF01589103⟩. ⟨halshs-00585327⟩