A truncated projected SVD method for linear discrete ill-posed problems

Numerical Algorithms

Volumn 43, Issue 3, 2006, Pages 197-213

  Morigi, Serena ^a   Reichel, Lothar ^b   Sgallari, Fiorella ^a  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b KENT STATE UNIVERSITY   (United States)

Author keywords

Decomposition; Ill posed problem; Inverse problem; SVD; TSVD

Indexed keywords

EID: 33847303943     PISSN: 10171398     EISSN: 15729265     Source Type: Journal    
DOI: 10.1007/s11075-006-9053-3     Document Type: Article

References (11)

1. Baglama, J., Reichel, L.: Decomposition methods for large linear discrete ill-posed problems. J. Comput. Appl. Math. 198, 332-343 (2007)
2. Calvetti, D., Lewis, B., Reichel, L.: GMRES, L-curves and discrete ill-posed problems. BIT 42, 44-65 (2002)
3. Eidén, L.: Partial least squares vs. Lanczos bidiagonalization. I. Analysis of a projection method for multiple regression. Comput. Stat. Data Anal. 46, 11-31 (2004)
4. Golub, G.H., Van Loan, CF.: Matrix Computations, 3rd ed. Johns Hopkins University Press, Baltimore, MD (1996)
5. Hansen, P.C.: Regularization, GSVD and truncated GSVD. BIT 29, 491-504 (1989)
6. Hansen, P.C.: Truncated SVD solutions to discrete ill-posed problems with ill-determined numerical rank. SIAM J. Sci. Stat. Comput. 11, 503-518 (1990)
7. Hansen, P.C.: Regularization tools: a Matlab package for analysis and solution of discrete ill-posed problems. Numer. Algor. 6, 1-35 (1994)
8. Hansen, P.C.: Rank Deficient and Discrete Ill-posed Problems. SIAM, Philadelphia, PA (1998)
9. Hansen, P.C., Jacobsen, M., Rasmussen, J.M., Sørensen, H.: The PP-TSVD algorithm for image restoration problems. In: Hansen P.C., Jacobsen H.H., Mosegaard K. (eds.) Methods and Applications of Inversion. Lecture Notes in Earth Sciences 92, pp. 171-202. Springer, Berlin Heidelberg New York (2000)
10. Hansen, P.C., Sekii, T., Shibahashi, H.: The modified truncated SVD method for regularization in general form. SIAM J. Sci. Stat. Comput. 13, 1142-1150 (1992)
11. Paige, C.C.: Computing the generalized singular value decomposition. SIAM J. Sci. Stat. Comput. 7, 1126-1146 (1986)