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

Authors:
Michiel E. Hochstenbach;Lothar Reichel
Affiliations:
Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB, The Netherlands;Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 8
Cited 1

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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.