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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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
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Abstract	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.
AbstractList	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.
Author	Reichel, Lothar Hochstenbach, Michiel E.
Author_xml	– sequence: 1 givenname: Michiel E. surname: Hochstenbach fullname: Hochstenbach, Michiel E. organization: Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB, The Netherlands – sequence: 2 givenname: Lothar surname: Reichel fullname: Reichel, Lothar email: reichel@math.kent.edu organization: Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA
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Cites_doi	10.1016/S0377-0427(03)00497-7 10.1093/imanum/2.2.241 10.1023/A:1021918118380 10.1007/BF02219234 10.1137/0911028 10.1007/s11075-006-9053-3 10.1007/s11075-007-9136-9 10.1109/TAC.2005.858651 10.1016/S0167-9473(03)00138-5 10.1137/0913066
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Keywords	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
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SubjectTerms	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
Title	Subspace-restricted singular value decompositions for linear discrete ill-posed problems
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