19th GAMM-Seminar Leipzig on
High-dimensional problems - Numerical treatment and applications

Max-Planck-Institute for Mathematics in the Sciences
Inselstr. 22-26, D-04103 [O->]Leipzig
Phone: +49.341.9959.752, Fax: +49.341.9959.999

  19th GAMM-Seminar
January, 23th-25th, 2003
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  Abstract Ilgis Ibragimow, Sat, 11.00-11.25 Previous Contents Next  
  Three-way decomposition and its applications
Ilgis Ibragimow (Uni Saarbrücken)

In this talk we discuss the decomposition of tex2html_wrap_inline15, tex2html_wrap_inline17, as tex2html_wrap_inline19 in the Frobenius norm, where tex2html_wrap_inline21 and tex2html_wrap_inline23 have normalized columns, E and tex2html_wrap_inline27 are diagonal and tex2html_wrap_inline29 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 tex2html_wrap_inline35 have exact decomposition, then we can construct an algorithm for this decomposition with about tex2html_wrap_inline37 arithmetical operations. This algorithm is important for preconditioning of dense matrices created from 2D and 3D integral operators. An implementation of the numerical algorithm was developed, several examples were tested and good results obtained.

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Last updated:
30.11.2004 Impressum
Concept, Design and Realisation
[O->]Jens Burmeister (Uni Kiel), Kai Helms (MPI Leipzig)
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