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.

Date Published: 4 September 2009
PDF: 12 pages
Proc. SPIE 7446, Wavelets XIII, 744611 (4 September 2009); doi: 10.1117/12.825303

Published in SPIE Proceedings Vol. 7446:
Wavelets XIII
Vivek K. Goyal; Manos Papadakis; Dimitri Van De Ville, Editor(s)