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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:235

Article; Proceedings Paper

Hochstenbach, Michiel E.²  Reichel, Lothar¹ 

[1] Kent State Univ, Dept Math Sci, Kent, OH 44242 USA

[2] Eindhoven Univ Technol, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands

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

DOI  :  10.1016/j.cam.2010.06.016

来源: Elsevier

【 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.

【 授权许可】

Free