کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5776237 | 1631969 | 2017 | 11 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Global Golub-Kahan bidiagonalization applied to large discrete ill-posed problems Global Golub-Kahan bidiagonalization applied to large discrete ill-posed problems](/preview/png/5776237.png)
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 Golub-Kahan 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 Golub-Kahan bidiagonalization and Gauss-type quadrature rules is exploited to inexpensively compute bounds that are useful for determining the regularization parameter by the discrepancy principle.
Journal: Journal of Computational and Applied Mathematics - Volume 322, 1 October 2017, Pages 46-56