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Preprint (Vorabdruck) zugänglich unter
SVD-like decomposition with constraints
URN: urn:nbn:de:bsz:291-scidok-43345
URL: http://scidok.sulb.uni-saarland.de/volltexte/2011/4334/
pdf-Format:
Dokument 1.pdf (166 KB)
Institut:
Fachrichtung 6.1 - Mathematik
DDC-Sachgruppe:
Mathematik
Dokumentart:
Preprint (Vorabdruck)
Schriftenreihe:
Preprint / Fachrichtung Mathematik, Universität des Saarlandes
Bandnummer:
26
Sprache:
Englisch
Erstellungsjahr:
2001
Publikationsdatum:
22.11.2011
Kurzfassung auf Englisch:
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.
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