A truncated projected SVD method for linear discrete ill-posed problems |
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Authors: | Serena Morigi Lothar Reichel Fiorella Sgallari |
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Affiliation: | (1) Department of Mathematics, University of Bologna, Piazza Porta S. Donato 5, 40127 Bologna, Italy;(2) Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA;(3) CIRAM Department of Mathematics, University of Bologna, Via Saragozza 8, 40123 Bologna, Italy |
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Abstract: | Truncated singular value decomposition is a popular solution method for linear discrete ill-posed problems. However, since the singular value decomposition of the matrix is independent of the right-hand side, there are linear discrete ill-posed problems for which this method fails to yield an accurate approximate solution. This paper describes a new approach to incorporating knowledge about properties of the desired solution into the solution process through an initial projection of the linear discrete ill-posed problem. The projected problem is solved by truncated singular value decomposition. Computed examples illustrate that suitably chosen projections can enhance the accuracy of the computed solution. |
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Keywords: | ill-posed problem inverse problem decomposition SVD TSVD |
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