Scalable frames
Copyright policy )Scalable frames
Tight frames can be characterized as those frames which possess optimal numerical stability properties. In this paper, we consider the question of modifying a general frame to generate a tight frame by rescaling its frame vectors; a process which can also be regarded as perfect preconditioning of a frame by a diagonal operator. A frame is called scalable, if such a diagonal operator exists. We derive various characterizations of scalable frames, thereby including the infinite-dimensional situation. Finally, we provide a geometric interpretation of scalability in terms of conical surfaces.
19 pages
FOS: Computer and information sciences, Numerical Analysis, Algebra and Number Theory, Computer Science - Information Theory, Information Theory (cs.IT), General harmonic expansions, frames, Numerical Analysis (math.NA), Functional Analysis (math.FA), Mathematics - Functional Analysis, numerical stability, FOS: Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematics - Numerical Analysis, diagonal operator, 12D10, 14P05, 15A03, 15A12, 42C15, 65F08
FOS: Computer and information sciences, Numerical Analysis, Algebra and Number Theory, Computer Science - Information Theory, Information Theory (cs.IT), General harmonic expansions, frames, Numerical Analysis (math.NA), Functional Analysis (math.FA), Mathematics - Functional Analysis, numerical stability, FOS: Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematics - Numerical Analysis, diagonal operator, 12D10, 14P05, 15A03, 15A12, 42C15, 65F08
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