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The iterative proportional fitting procedure (IPFP), introduced in 1937 by Kruithof, aims to adjust the elements of an array to satisfy specified row and column sums. Thus, given a rectangular non-negative matrix X0 and two positive marginals a and b, the algorithm generates a sequence of matrices (Xn)n≥0 starting at X0, supposed to converge to a biproportional fitting, that is, to a matrix Y whose marginals are a and b and of the form Y = D1X0D2, for some diagonal matrices D1 and D2 with positive diagonal entries.

Iterated Proportional Fitting Procedure and Infinite Products of Stochastic Matrices