The conjugate gradient algorithm applied to quaternion valued matrices

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Autor/in:
Erscheinungsjahr:
2005
Medientyp:
Text
Schlagworte:
  • Conjugate gradient algorithm
  • Linear systems of equations with quaternion coefficients
  • Quaternion valued matrices
  • cg-algorithm
Beschreibung:
  • Quaternions are a tool used to describe motions of rigid bodies in ℝ3, (Kuipers, [15]). An interesting application is the topic of moving surfaces (Traversoni, [21]), where quaternion interpolation is used which requires solving equations with quaternion coefficients. In this paper we investigate the well known conjugate gradient algorithm (cg-algorithm) introduced by Hestenes and Stiefel [10] applied to quaternion valued, hermitean, positive definite matrices. We shall show, that the features known from the real case are still valid in the quaternion case. These features are: error propagation, early stopping, cg-algorithm as iterative process with error estimates, applicability to indefinite matrices. We have to present some basic facts about quaternions and about matrices with quaternion entries, in particular, about eigenvalues of such matrices. We also present some numerical examples of quaternion systems solved by the cg-algorithm. © 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Lizenz:
  • info:eu-repo/semantics/closedAccess
Quellsystem:
Forschungsinformationssystem der UHH
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oai:www.edit.fis.uni-hamburg.de:publications/84e0876a-4889-4793-ad4c-6d7512eb4575