Dr. Peter Oswald Profile

Dr. Peter Oswald

at Jacobs Univ Bremen

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Proceedings Article | 4 September 2009 Paper

Stable space splittings and fusion frames

Peter Oswald

Proceedings Volume 7446, 744611 (2009) https://doi.org/10.1117/12.825303

KEYWORDS: Space operations, Iterative methods, Condition numbers, Chemical elements, Wavelets, Gold, Distributed computing, Hassium, Finite element methods, Particles

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The concept of stable space splittings has been introduced in the early 1990ies, as a convenient framework for developing a unified theory of iterative methods for variational problems in Hilbert spaces, especially for solving large-scale discretizations of elliptic problems in Sobolev spaces. The more recently introduced notions of frames of subspaces and fusion frames turn out to be concrete instances of stable space splittings. However, driven by applications to robust distributed signal processing, their study has focused so far on different aspects. The paper surveys the existing results on stable space splittings and iterative methods, outlines the connection to fusion frames, and discusses the investigation of quarkonial or multilevel partition-of-unity frames as an example of current interest.

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