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 hdl:20.500.11880/26241 http://dx.doi.org/10.22028/D291-26185 |
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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preprint_26_01.pdf | 165,54 kB | Adobe PDF | View/Open |
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