Implicit iteration methods in Hilbert scales under general smoothness conditions
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Jin, Qinian; Tautenhahn, Ulrich
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For solving linear ill-posed problems, regularization methods are required when the right-hand side is with some noise. In this paper regularized solutions are obtained by implicit iteration methods in Hilbert scales. By exploiting operator monotonicity of certain functions and interpolation techniques in variable Hilbert scales, we study these methods under general smoothness conditions. Order optimal error bounds are given in case the regularization parameter is chosen either a priori or a...[Show more]
dc.contributor.author | Jin, Qinian | |
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dc.contributor.author | Tautenhahn, Ulrich | |
dc.date.accessioned | 2015-12-07T22:53:52Z | |
dc.identifier.issn | 0266-5611 | |
dc.identifier.uri | http://hdl.handle.net/1885/27913 | |
dc.description.abstract | For solving linear ill-posed problems, regularization methods are required when the right-hand side is with some noise. In this paper regularized solutions are obtained by implicit iteration methods in Hilbert scales. By exploiting operator monotonicity of certain functions and interpolation techniques in variable Hilbert scales, we study these methods under general smoothness conditions. Order optimal error bounds are given in case the regularization parameter is chosen either a priori or a posteriori by the discrepancy principle. For realizing the discrepancy principle, some fast algorithm is proposed which is based on Newton's method applied to some properly transformed equations. | |
dc.publisher | Institute of Physics Publishing | |
dc.source | Inverse Problems | |
dc.subject | Keywords: Discrepancy principle; Fast algorithms; Hilbert scale; Interpolation techniques; Iteration method; Linear ill-posed problems; Monotonicity; Newton's methods; Optimal error bound; Posteriori; Regularization methods; Regularization parameters; Right-hand si | |
dc.title | Implicit iteration methods in Hilbert scales under general smoothness conditions | |
dc.type | Journal article | |
local.description.notes | Imported from ARIES | |
local.identifier.citationvolume | 27 | |
dc.date.issued | 2011 | |
local.identifier.absfor | 010102 - Algebraic and Differential Geometry | |
local.identifier.ariespublication | u5035478xPUB54 | |
local.type.status | Published Version | |
local.contributor.affiliation | Jin, Qinian, College of Physical and Mathematical Sciences, ANU | |
local.contributor.affiliation | Tautenhahn, Ulrich, University of Applied Sciences Zittau/Görlitz | |
local.description.embargo | 2037-12-31 | |
local.bibliographicCitation.issue | 4 | |
local.bibliographicCitation.startpage | 1 | |
local.bibliographicCitation.lastpage | 27 | |
local.identifier.doi | 10.1088/0266-5611/27/4/045012 | |
dc.date.updated | 2016-02-24T11:33:37Z | |
local.identifier.scopusID | 2-s2.0-79953660521 | |
local.identifier.thomsonID | 000288696200012 | |
Collections | ANU Research Publications |
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