Three-way decomposition and its applications
Ilgis Ibragimow (Uni Saarbrücken)
In this talk we discuss the decomposition of , ,
as in the Frobenius norm, where
and have normalized columns, E and are
diagonal and is the identity matrix.
This decomposition is widely used in the data processing and is the
generalization of the singular value decomposition for the 3-dimensional
case. Additionally we discuss a case when B, C have full column rank.
If have exact decomposition, then we can construct an algorithm for
this decomposition with about arithmetical operations. This algorithm
is important for preconditioning of dense matrices created from 2D and 3D integral
An implementation of the numerical algorithm was developed, several
examples were tested and good results obtained.