Combining approximate solutions for linear discrete ill-posed problems

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...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2012-02, Vol.236 (8), p.2179-2185
Main Authors: Hochstenbach, Michiel E., Reichel, Lothar
Format: Article
Language:English
Subjects:
Approximation
Computation
Decomposition
Discrepancy principle
Ill posed problems
Ill-posed problem
Linear combination
Mathematical models
Numerical analysis
Regularization
Solution norm constraint
Tikhonov regularization
TSVD
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Summary: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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2011.09.040