Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 727-742 |
| Seitenumfang | 16 |
| Fachzeitschrift | Discrete and Computational Geometry |
| Jahrgang | 56 |
| Ausgabenummer | 3 |
| Publikationsstatus | Veröffentlicht - 1 Okt. 2016 |
Abstract
Hilbert space frames generalize orthonormal bases to allow redundancy in representations of vectors while keeping good reconstruction properties. A frame comes with an associated frame operator encoding essential properties of the frame. We study a polytope that arises in an algorithm for constructing all finite frames with given lengths of frame vectors and spectrum of the frame operator, which is a Gelfand–Tsetlin polytope. For equal norm tight frames, we give a non-redundant description of the polytope in terms of equations and inequalities. From this we obtain the dimension and number of facets of the polytope. While studying the polytope, we find two affine isomorphisms and show how they relate to operations on the underlying frames.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Theoretische Informatik
- Mathematik (insg.)
- Geometrie und Topologie
- Mathematik (insg.)
- Diskrete Mathematik und Kombinatorik
- Informatik (insg.)
- Theoretische Informatik und Mathematik
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in: Discrete and Computational Geometry, Jahrgang 56, Nr. 3, 01.10.2016, S. 727-742.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Polytopes of Eigensteps of Finite Equal Norm Tight Frames
AU - Haga, Tim
AU - Pegel, Christoph
N1 - Publisher Copyright: © 2016, Springer Science+Business Media New York. Copyright: Copyright 2016 Elsevier B.V., All rights reserved.
PY - 2016/10/1
Y1 - 2016/10/1
N2 - Hilbert space frames generalize orthonormal bases to allow redundancy in representations of vectors while keeping good reconstruction properties. A frame comes with an associated frame operator encoding essential properties of the frame. We study a polytope that arises in an algorithm for constructing all finite frames with given lengths of frame vectors and spectrum of the frame operator, which is a Gelfand–Tsetlin polytope. For equal norm tight frames, we give a non-redundant description of the polytope in terms of equations and inequalities. From this we obtain the dimension and number of facets of the polytope. While studying the polytope, we find two affine isomorphisms and show how they relate to operations on the underlying frames.
AB - Hilbert space frames generalize orthonormal bases to allow redundancy in representations of vectors while keeping good reconstruction properties. A frame comes with an associated frame operator encoding essential properties of the frame. We study a polytope that arises in an algorithm for constructing all finite frames with given lengths of frame vectors and spectrum of the frame operator, which is a Gelfand–Tsetlin polytope. For equal norm tight frames, we give a non-redundant description of the polytope in terms of equations and inequalities. From this we obtain the dimension and number of facets of the polytope. While studying the polytope, we find two affine isomorphisms and show how they relate to operations on the underlying frames.
KW - Combinatorics
KW - Convex geometry
KW - Hilbert space frames
KW - Polytopes
UR - http://www.scopus.com/inward/record.url?scp=84976415962&partnerID=8YFLogxK
U2 - 10.1007/s00454-016-9799-x
DO - 10.1007/s00454-016-9799-x
M3 - Article
VL - 56
SP - 727
EP - 742
JO - Discrete and Computational Geometry
JF - Discrete and Computational Geometry
SN - 0179-5376
IS - 3
ER -