biproportional

biproportional

English

Etymology

bi- +‎ proportional

Adjective

biproportional (not comparable)

1. (mathematics) Providing two-way proportionality.
   • 2016, Jean Brossard, Christophe Leuridan, “Iterated proportional fitting procedure and infinite products of stochastic matrices”, in arXiv‎:

     Given a rectangular non-negative matrix ${\\displaystyle X_{0}}$ and two positive marginals ${\\displaystyle a}$ and ${\\displaystyle b}$, the algorithm generates a sequence of matrices ${\\displaystyle (X_{n})}$ starting at ${\\displaystyle X_{0}}$, supposed to converge to a biproportional fitting, that is, to a matrix ${\\displaystyle Y}$ whose marginals are ${\\displaystyle a}$ and ${\\displaystyle b}$ and of the form ${\\displaystyle Y=D_{1}X_{0}D_{2}}$, for some diagonal matrices ${\\displaystyle D_{1}}$ and ${\\displaystyle D_{2}}$ with positive diagonal entries. When a biproportional fitting does exist, it is unique and the sequence ${\\displaystyle (X_{n})}$ converges to it at an at least geometric rate.