Kybernetika 39 no. 6, 731-737, 2003

A note on the IPF algorithm when the marginal problem is unsolvable

Claudio Asci and Mauro Piccioni


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.