@phdthesis{Curtef2012,
  author    = {Curtef, Oana},
  title     = {Rayleigh-quotient optimization on tensor products of Grassmannians},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-83383},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2012},
  abstract  = {Applications in various research areas such as signal processing, quantum computing, and computer vision, can be described as constrained optimization tasks on certain subsets of tensor products of vector spaces. In this work, we make use of techniques from Riemannian geometry and analyze optimization tasks on subsets of so-called simple tensors which can be equipped with a differentiable structure. In particular, we introduce a generalized Rayleigh-quotient function on the tensor product of Grassmannians and on the tensor product of Lagrange- Grassmannians. Its optimization enables a unified approach to well-known tasks from different areas of numerical linear algebra, such as: best low-rank approximations of tensors (data compression), computing geometric measures of entanglement (quantum computing) and subspace clustering (image processing). We perform a thorough analysis on the critical points of the generalized Rayleigh-quotient and develop intrinsic numerical methods for its optimization. Explicitly, using the techniques from Riemannian optimization, we present two type of algorithms: a Newton-like and a conjugated gradient algorithm. Their performance is analysed and compared with established methods from the literature.},
  subject      = {Optimierung},
  language  = {en}
}