Name
Abstract | ||
|---|---|---|
We consider the solution of large linear systems of equations that arise from the discretization of ill-posed problems. The matrix has a Kronecker product structure and the right-hand side is contaminated by measurement error. Problems of this kind arise, for instance, from the discretization of Fredholm integral equations of the first kind in two space-dimensions with a separable kernel and in image restoration problems. Regularization methods, such as Tikhonov regularization, have to be employed to reduce the propagation of the error in the right-hand side into the computed solution. We investigate the use of the global GolubKahan bidiagonalization method to reduce the given large problem to a small one. The small problem is solved by employing Tikhonov regularization. A regularization parameter determines the amount of regularization. The connection between global GolubKahan bidiagonalization and Gauss-type quadrature rules is exploited to inexpensively compute bounds that are useful for determining the regularization parameter by the discrepancy principle. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.cam.2017.03.016 | J. Computational Applied Mathematics |
Keywords | Field | DocType |
Global Golub–Kahan bidiagonalization,Ill-posed problems,Gauss quadrature | Tikhonov regularization,Discretization,Mathematical optimization,Well-posed problem,Kronecker product,Mathematical analysis,Backus–Gilbert method,Bidiagonalization,Regularization (mathematics),Mathematics,Regularization perspectives on support vector machines | Journal |
Volume | Issue | ISSN |
322 | C | 0377-0427 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| A. H. Bentbib | 1 | 7 | 0.87 |
| M. El Guide | 2 | 7 | 0.87 |
| Khalide Jbilou | 3 | 38 | 12.08 |
| Lothar Reichel | 4 | 453 | 95.02 |