Geodesic
A note on the IPF algorithm when the marginal problem is unsolvable
Kybernetika, Tome 39 (2003) no. 6, p. [731].

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In this paper we analyze the asymptotic behavior of the IPF algorithm for the problem of finding a 2x2x2 contingency table whose pair marginals are all equal to a specified 2x2 table, depending on a parameter. When this parameter lies below a certain threshold the marginal problem has no solution. We show that in this case the IPF has a “period three limit cycle” attracting all positive initial tables, and a bifurcation occur when the parameter crosses the threshold.
Classification : 62H17, 65C60
Keywords: contingency tables; hierarchical models; partial maximization algorithms 
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     author = {Asci, Claudio and Piccioni, Mauro},
     title = {A note on the {IPF} algorithm when the marginal problem is unsolvable},
     journal = {Kybernetika},
     pages = {[731]},
     publisher = {mathdoc},
     volume = {39},
     number = {6},
     year = {2003},
     mrnumber = {2035647},
     zbl = {1245.62070},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2003__39_6_a4/}
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Asci, Claudio; Piccioni, Mauro. A note on the IPF algorithm when the marginal problem is unsolvable. Kybernetika, Tome 39 (2003) no. 6, p. [731]. http://geodesic.mathdoc.fr/item/KYB_2003__39_6_a4/