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Error minimizing relaxation strategies in Landweber and Kaczmarz type iterations
Iran University of Science and Technology, Iran; Institute Research Fundamental Science IPM, Iran.
Iran University of Science and Technology, Iran.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
2017 (English)In: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945, Vol. 25, no 1, 35-56 p.Article in journal (Refereed) Published
Abstract [en]

We study error minimizing relaxation (EMR) strategies for use in Landweber and Kaczmarz type iterations applied to linear systems with or without convex constraints. Convergence results based on operator theory are given, assuming exact data. The advantages and disadvantages of these relaxation strategies on a noisy and ill-posed problem are illustrated using examples taken from the field of image reconstruction from projections. We also consider combining EMR with penalization.

Place, publisher, year, edition, pages
WALTER DE GRUYTER GMBH , 2017. Vol. 25, no 1, 35-56 p.
Keyword [en]
Simultaneous and sequential block algorithm; Kaczmarzs and Landweber iterations; steepest decent; relaxation parameters (step size); tomography; image reconstruction from projections
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-136174DOI: 10.1515/jiip-2015-0082ISI: 000394001800003OAI: oai:DiVA.org:liu-136174DiVA: diva2:1086656
Note

Funding Agencies|IPM [94650073]

Available from: 2017-04-03 Created: 2017-04-03 Last updated: 2017-04-03

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