Noise representation in residuals of LSQR, LSMR, and CRAIG regularization

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dc.contributor.authorPlešinger Martincs
dc.contributor.authorHnětynková Ivetacs
dc.contributor.authorKubínová Mariecs
dc.date.accessioned2018-09-25T12:15:45Z
dc.date.available2018-09-25T12:15:45Z
dc.date.issued2017-11-15cs
dc.description.abstractGolub–Kahan iterative bidiagonalization represents the core algorithm in several regularization methods for solving large linear noise-polluted ill-posed problems. We consider a general noise setting and derive explicit relations between (noise contaminated) bidiagonalization vectors and the residuals of bidiagonalization-based regularization methods LSQR, LSMR, and CRAIG. For LSQR and LSMR residuals we prove that the coefficients of the linear combination of the computed bidiagonalization vectors reflect the amount of propagated noise in each of these vectors. For CRAIG the residual is only a multiple of a particular bidiagonalization vector. We show how its size indicates the regularization effect in each iteration by expressing the CRAIG solution as the exact solution to a modified compatible problem. Validity of the results for larger two-dimensional problems and influence of the loss of orthogonality is also discussed.cs
dc.format.extent23cs
dc.identifier.doi10.1016/j.laa.2017.07.031
dc.identifier.issn0024-3795cs
dc.identifier.urihttps://dspace.tul.cz/handle/15240/31433
dc.identifier.urihttps://www.sciencedirect.com/science/article/pii/S0024379517304512?via%3Dihub
dc.language.isoengcs
dc.publisherElseviercs
dc.relation.ispartofseries0cs
dc.relation.urihttps://www.sciencedirect.com/science/article/pii/S0024379517304512cs
dc.subjectIll-posed problemscs
dc.subjectRegularizationcs
dc.subjectGolub&#8211cs
dc.subjectKahan iterative bidiagonalizationcs
dc.subjectLSQRcs
dc.subjectLSMRcs
dc.subjectCRAIGcs
dc.titleNoise representation in residuals of LSQR, LSMR, and CRAIG regularizationen
local.citation.epage357-379cs
local.citation.spage357-379cs
local.identifier.publikace4896
local.identifier.wok412965500017en
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