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On the exponential convergence of the Kaczmarz algorithm
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
2015 (English)In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 22, no 10, 1571-1574 p.Article in journal (Refereed) Published
Abstract [en]

The Kaczmarz algorithm (KA) is a popular method for solving a system of linear equations. In this note we derive a new exponential convergence result for the KA. The key allowing us to establish the new result is to rewrite the KA in such a way that its solution path can be interpreted as the output from a particular dynamical system. The asymptotic stability results of the corresponding dynamical system can then be leveraged to prove exponential convergence of the KA. The new bound is also compared to existing bounds.

Place, publisher, year, edition, pages
2015. Vol. 22, no 10, 1571-1574 p.
National Category
Signal Processing
Identifiers
URN: urn:nbn:se:uu:diva-252154DOI: 10.1109/LSP.2015.2412253ISI: 000352088600009OAI: oai:DiVA.org:uu-252154DiVA: diva2:810513
Available from: 2015-03-25 Created: 2015-05-04 Last updated: 2017-12-04Bibliographically approved

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Dai, LiangSchön, Thomas B.

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