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Computational solutions of a family of generalized Procrustes problems

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.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-qucosa-146840
Date30 June 2014
CreatorsFankhänel, Jens, Benner, Peter
ContributorsTU Chemnitz, Fakultät für Mathematik
PublisherUniversitätsbibliothek Chemnitz
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:preprint
Formatapplication/pdf, text/plain, application/zip
Relationdcterms:isPartOf:Preprintreihe der Fakultät für Mathematik der TU Chemnitz, Preprint 2014-06

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