biproportionalとは 意味・読み方・使い方

形容詞

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^[1]:

     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.