Abstract.
Biproportional methods are used to update matrices: the projection of a matrix Z to give it the column and row sums of another matrix is R Z S, where R and S are diagonal and secure the constraints of the problem (R and S have no signification at all because they are not identified). However, normalizing R or S generates important mathematical difficulties: it amounts to put constraints on Lagrange multipliers, non negativity (and so the existence of the solution) is not guaranteed at equilibrium or along the path to equilibrium.
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Received: June 2001/Accepted: September 2001
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de Mesnard, L. Normalizing biproportional methods. Ann Reg Sci 36, 139–144 (2002). https://doi.org/10.1007/s001680100070
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DOI: https://doi.org/10.1007/s001680100070