Please use this identifier to cite or link to this item: doi:10.22028/D291-26185
Title: SVD-like decomposition with constraints
Author(s): Ibraghimov, Ilghiz
Language: English
Year of Publication: 2001
DDC notations: 510 Mathematics
Publikation type: Other
Abstract: 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.
Link to this record: urn:nbn:de:bsz:291-scidok-43345
Series name: Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Series volume: 26
Date of registration: 22-Nov-2011
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Collections:SciDok - Der Wissenschaftsserver der Universität des Saarlandes

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