Geodesic
Tikhonov regularization with nonnegativity constraint
Electronic transactions on numerical analysis, Tome 18 (2004), pp. 153-173
Many numerical methods for the solution of ill-posed problems are based on Tikhonov regularization. Recently, Rojas and Steihaug [15] described a barrier method for computing nonnegative Tikhonov-regularized approximate solutions of linear discrete ill-posed problems. Their method is based on solving a sequence of parameterized eigenvalue problems. This paper describes how the solution of parametrized eigenvalue problems can be avoided by computing bounds that follow from the connection between the Lanczos process, orthogonal polynomials and Gauss quadrature.
Classification : 65F22, 65F10, 65R30, 65R32, 65R20
Keywords: ill-posed problem, inverse problem, solution constraint, Lanczos methods, Gauss quadrature 
@article{ETNA_2004__18__a3,
     author = {Calvetti,  D. and Lewis,  B. and Reichel,  L. and Sgallari,  F.},
     title = {Tikhonov regularization with nonnegativity constraint},
     journal = {Electronic transactions on numerical analysis},
     pages = {153--173},
     year = {2004},
     volume = {18},
     zbl = {1069.65047},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2004__18__a3/}
}
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EP  - 173
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UR  - http://geodesic.mathdoc.fr/item/ETNA_2004__18__a3/
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%A Sgallari,  F.
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%J Electronic transactions on numerical analysis
%D 2004
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%U http://geodesic.mathdoc.fr/item/ETNA_2004__18__a3/
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%F ETNA_2004__18__a3
Calvetti,  D.; Lewis,  B.; Reichel,  L.; Sgallari,  F. Tikhonov regularization with nonnegativity constraint. Electronic transactions on numerical analysis, Tome 18 (2004), pp. 153-173. http://geodesic.mathdoc.fr/item/ETNA_2004__18__a3/