Subspace-restricted singular value decompositions for linear discrete ill-posed problems

The truncated singular value decomposition is a popular solution method for linear discrete ill-posed problems. These problems are numerically underdetermined. Therefore, it can be beneficial to incorporate information about the desired solution into the solution process. This paper describes a modi...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 235; no. 4; pp. 1053 - 1064
Main Authors: Hochstenbach, Michiel E., Reichel, Lothar
Format: Journal Article Conference Proceeding
Language:English
Published: Kidlington Elsevier B.V 15.12.2010
Elsevier
Subjects:
Computation
Decomposition
Exact sciences and technology
Ill posed problems
Ill-posed problem
Inverse problem
Mathematical analysis
Mathematical models
Mathematics
Modified SVD
Numerical analysis
Numerical analysis in abstract spaces
Numerical analysis. Scientific computation
Numerical linear algebra
Sciences and techniques of general use
SRSVD
Subspaces
Tikhonov regularization
TSVD
65R32
Modified SVD
65R30
65F10
Ill-posed problem
TSVD
SRSVD
Tikhonov regularization
Inverse problem
Numerical linear algebra
Truncation
Regularization method
Numerical analysis
Applied mathematics
Ill posed problem
III-posed problem
Singular value decomposition
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Summary:The truncated singular value decomposition is a popular solution method for linear discrete ill-posed problems. These problems are numerically underdetermined. Therefore, it can be beneficial to incorporate information about the desired solution into the solution process. This paper describes a modification of the singular value decomposition that permits a specified linear subspace to be contained in the solution subspace for all truncations. Modifications that allow the range to contain a specified subspace, or that allow both the solution subspace and the range to contain specified subspaces also are described.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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content type line 23
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2010.06.016