Combining approximate solutions for linear discrete ill-posed problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:236

Article

Hochstenbach, Michiel E.¹  Reichel, Lothar² 

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

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

关键词: Ill-posed problem;    Linear combination;    Solution norm constraint;    TSVD;    Tikhonov regularization;    Discrepancy principle;   

DOI  :  10.1016/j.cam.2011.09.040

来源: Elsevier

【 摘 要 】

Linear discrete ill-posed problems of small to medium size are commonly solved by first computing the singular value decomposition of the matrix and then determining an approximate solution by one of several available numerical methods, such as the truncated singular value decomposition or Tikhonov regularization. The determination of an approximate solution is relatively inexpensive once the singular value decomposition is available. This paper proposes to compute several approximate solutions by standard methods and then extract a new candidate solution from the linear subspace spanned by the available approximate solutions. We also describe how the method may be used for large-scale problems. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free