TY  - GEN
T1  - SVD-like decomposition with constraints
A1  - Ibraghimov,Ilghiz
Y1  - 2011/11/22
N2  - We search for the best fit in Frobenius norm of A\in\mathbb{C}^{mxn} by a matrix product BC*, where B\in\mathbb{C}^{mxr} and C\in\mathbb{C}^{nxr}, r\leq m so B=\{b_{i,j}\}_{{i=1,...,m\atop j=1,...,r}} definite by some unknown parameters \sigma_{1},...,\sigma_{k}, k<<mr and all partial derivatives of \frac{\delta b_{ij}}{\delta\sigma_{l}} are definite, bounded and can be computed analytically.
We show that this problem transforms to a new minimization problem with only k unknowns, with analytical computation of gradient of minimized function by all \sigma. The complexity of computation of gradient is only 4 times bigger than the complexity of computation of the function, and this new algorithm needs only 3mr additional memory. 
We apply this approach for solution of the three-way decomposition problem and obtain good results of convergence of Broyden algorithm.
CY  - Saarbrücken
PB  - Universitäts- und Landesbibliothek
AD  - Postfach 151141, 66041 Saarbrücken
UR  - http://scidok.sulb.uni-saarland.de/volltexte/2011/4334
ER  -