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

[摘要] 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. (C) 2010 Elsevier B.V. All rights reserved.

[发布日期] 2010-12-15

[效力级别]  Proceedings Paper

[关键词] Ill-posed problem;Inverse problem;Modified SVD;TSVD;SRSVD;Tikhonov regularization