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SOME NUMERICAL RESULTS ON THE RANK OF GENERIC THREE-WAY ARRAYS OVER R.
- Source :
-
SIAM Journal on Matrix Analysis & Applications . 2010, Vol. 31 Issue 4, p1541-1551. 11p. 4 Charts. - Publication Year :
- 2010
-
Abstract
- The aim of this paper is the introduction of a new method for the numerical computation of the rank of a three-way array X ∈ RI×J×K over R. We show that the rank of a three-way array over R is intimately related to the real solution set of a system of polynomial equations. Using this, we present some numerical results based on the computation of Gr¨obner bases. Also, we show that for I = (K − 1)(J − 1) + 1 and 2 ≤ K ≤ J ≤ I, the rank for generic data has more than one rank value, and the minimum attained value is I. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 08954798
- Volume :
- 31
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- SIAM Journal on Matrix Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 56563138
- Full Text :
- https://doi.org/10.1137/08073531X