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Exploiting tensor rank-one decomposition in probabilistic inference

Petr Savický, Jiří Vomlel (2007)

Kybernetika

We propose a new additive decomposition of probability tables – tensor rank-one decomposition. The basic idea is to decompose a probability table into a series of tables, such that the table that is the sum of the series is equal to the original table. Each table in the series has the same domain as the original table but can be expressed as a product of one- dimensional tables. Entries in tables are allowed to be any real number, i. e. they can be also negative numbers. The possibility of having...

Extreme points of the complex binary trilinear ball

Fernando Cobos, Thomas Kühn, Jaak Peetre (2000)

Studia Mathematica

We characterize all the extreme points of the unit ball in the space of trilinear forms on the Hilbert space 2 . This answers a question posed by R. Grząślewicz and K. John [7], who solved the corresponding problem for the real Hilbert space 2 . As an application we determine the best constant in the inequality between the Hilbert-Schmidt norm and the norm of trilinear forms.

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