Show simple item record

CAUCHY-LIKE PRECONDITIONERS FOR 2-DIMENSIONAL ILL-POSED PROBLEMS

dc.contributor.authorKilmer, Misha E.en_US
dc.date.accessioned2004-05-31T21:06:27Z
dc.date.available2004-05-31T21:06:27Z
dc.date.created1997-03en_US
dc.date.issued1998-10-15en_US
dc.identifier.urihttp://hdl.handle.net/1903/477
dc.description.abstractIll-conditioned matrices with block Toeplitz, Toeplitz block (BTTB) structure arise from the discretization of certain ill-posed problems in signal and image processing. We use a preconditioned conjugate gradient algorithm to compute a regularized solution to this linear system given noisy data. Our preconditioner is a Cauchy-like block diagonal approximation to an orthogonal transformation of the BTTB matrix. We show the preconditioner has desirable properties when the kernel of the ill-posed problem is smooth: the largest singular values of the preconditioned matrix are clustered around one, the smallest singular values remain small, and the subspaces corresponding to the largest and smallest singular values, respectively, remain unmixed. For a system involving $np$ variables, the preconditioned algorithm costs only $O(np (\lg n + \lg p))$ operations per iteration. We demonstrate the effectiveness of the preconditioner on three examples.en_US
dc.format.extent1003331 bytes
dc.format.mimetypeapplication/postscript
dc.language.isoen_US
dc.relation.ispartofseriesUM Computer Science Department; CS-TR-3776en_US
dc.titleCAUCHY-LIKE PRECONDITIONERS FOR 2-DIMENSIONAL ILL-POSED PROBLEMSen_US
dc.typeTechnical Reporten_US
dc.relation.isAvailableAtDigital Repository at the University of Marylanden_US
dc.relation.isAvailableAtUniversity of Maryland (College Park, Md.)en_US
dc.relation.isAvailableAtTech Reports in Computer Science and Engineeringen_US
dc.relation.isAvailableAtComputer Science Department Technical Reportsen_US


Files in this item

Thumbnail
Thumbnail

This item appears in the following Collection(s)

Show simple item record