- AutorIn
- Jens Fankhänel
- Prof. Dr. Peter Benner
- Titel
- Computational solutions of a family of generalized Procrustes problems
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:ch1-qucosa-143848
- Schriftenreihe
- Preprintreihe der Fakultät für Mathematik der TU Chemnitz, Preprint 2014-06
- ISSN
- 1614-8835
- Abstract (EN)
- We consider a family of generalized Procrustes problems. In this class of problems, one aims at aligning a set of vectors to a given second set of vectors. The distance between both sets is measured in the q norm, and for the alignment, isometries with respect to the p norm are allowed. In contrast to the classical Procrustes problem with p = q = 2, we allow p and q to differ. We will see that it makes a difference whether the problem is real or cast over the complex field. Therefore, we discuss the solutions for p = 2 separately for these cases. We show that all the real cases can be solved efficiently. Most of the complex cases can up to now only be solved approximately in polynomial time, but we show the existence of polynomial time algorithms for q ∈ {2, 4, ∞}. Computational experiments illustrate the suggested algorithms.
- Nachfolger
- Computational solutions of a family of generalized Procrustes problems
- Freie Schlagwörter (DE)
- Banachräume, Optimierung, verallgemeinerte Prokrustesprobleme, Normierte Räume, Lp-Räume
- Freie Schlagwörter (EN)
- Banach spaces, optimization, generalized Procrustes problems
- Klassifikation (DDC)
- 518
- Normschlagwörter (GND)
- Optimierung, Zuordnungsproblem
- Publizierende Institution
- Technische Universität Chemnitz, Chemnitz
- URN Qucosa
- urn:nbn:de:bsz:ch1-qucosa-143848
- Veröffentlichungsdatum Qucosa
- 02.06.2014
- Dokumenttyp
- Preprint
- Sprache des Dokumentes
- Englisch